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question_answer1)
A particle performs SHM in a straight line. In the first second, starting from rest, it travels a distance a and in the next second it travels a distance b in the same direction. The amplitude of the SHM is
A)
\[a-b\] done
clear
B)
\[\frac{2a-b}{3}\] done
clear
C)
\[\frac{2{{a}^{2}}}{3a-b}\] done
clear
D)
None of these done
clear
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question_answer2)
A simple harmonic oscillator of angular frequency \[2\,rad\,{{s}^{-1}}\] is acted upon by an external force F = sin t N. If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is given by:
A)
\[\sin \,t+\frac{1}{2}\cos \,2t\] done
clear
B)
\[\cos t-\frac{1}{2}\sin \,2t\] done
clear
C)
\[\sin t-\frac{1}{2}\sin \,2t\] done
clear
D)
\[\sin t+\frac{1}{2}\sin \,2t\] done
clear
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question_answer3)
Part of a simple harmonic motion is graphed in the figure, where y is the displacement from the mean position. The correct equation describing this S.H. M. is
A)
\[y=4\cos (0.6t)\] done
clear
B)
\[y=2\sin \left( \frac{10}{3}t+\frac{\pi }{2} \right)\] done
clear
C)
\[y=4\sin \left( \frac{10}{3}t+\frac{\pi }{2} \right)\] done
clear
D)
\[y=2\cos \left( \frac{10}{3}t+\frac{\pi }{2} \right)\] done
clear
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question_answer4)
If a is the amplitude of SHM, then K.E. is equal to the P.E. at............ distance from the mean position.
A)
\[\frac{a}{\sqrt{2}}\] done
clear
B)
\[\frac{a}{2}\] done
clear
C)
\[\frac{a}{4}\] done
clear
D)
\[a\] done
clear
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question_answer5)
Which of the following is true about total mechanical energy of SHM?
A)
It is zero at mean position. done
clear
B)
It is zero at extreme position. done
clear
C)
It is always zero. done
clear
D)
It is never zero. done
clear
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question_answer6)
In S.H. M. the ratio of kinetic energy at mean position to the potential energy when the displacement is half of the amplitude is
A)
\[\frac{4}{1}\] done
clear
B)
\[\frac{2}{3}\] done
clear
C)
\[\frac{4}{3}\] done
clear
D)
\[\frac{1}{2}\] done
clear
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question_answer7)
Starting from the origin a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?
A)
\[\frac{1}{6}s\] done
clear
B)
\[\frac{1}{4}s\] done
clear
C)
\[\frac{1}{3}s\] done
clear
D)
\[\frac{1}{12}s\] done
clear
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question_answer8)
For a particle executing SHM the displacement x is given by\[x=A\cos \,\omega t\]. Identify the graph which nrepresents the variation of potential energy (P. E.) as a function of time t and displacement x.
A)
I, III done
clear
B)
II, IV done
clear
C)
II, III done
clear
D)
I, IV done
clear
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question_answer9)
The total energy of the particle executing simple harmonic motion of amplitude A is 100 J. At a distance of 0.707 A from the mean position, its kinetic energy is
A)
25J done
clear
B)
50J done
clear
C)
100J done
clear
D)
12.5J done
clear
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question_answer10)
When the displacement of a particle executing simple harmonic motion is half of its amplitude, the ratio of its kinetic energy to potential energy
A)
1 : 3 done
clear
B)
2 : 1 done
clear
C)
3 : 1 done
clear
D)
1 : 2 done
clear
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question_answer11)
The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is
A)
\[\pi \] done
clear
B)
0.707\[\pi \] done
clear
C)
zero done
clear
D)
0.5\[\pi \] done
clear
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question_answer12)
A particle of mass 1 kg is moving in S.H.M. with an amplitude 0.02 and a frequency of 60 Hz. The maximum force acting on is
A)
144\[{{\pi }^{2}}\] done
clear
B)
188 \[{{\pi }^{2}}\] done
clear
C)
288\[{{\pi }^{2}}\] done
clear
D)
None of these done
clear
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question_answer13)
The displacement of a particle in simple harmonic motion in one time period is [A = amplitude]
A)
A done
clear
B)
2 A done
clear
C)
4 A done
clear
D)
Zero done
clear
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question_answer14)
Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel, the motion of the particle is
A)
simple harmonic done
clear
B)
parabolic done
clear
C)
oscillatory done
clear
D)
non-periodic done
clear
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question_answer15)
The acceleration of a particle undergoing SHM is graphed in figure. At point 2 the velocity of the particle is
A)
zero done
clear
B)
negative done
clear
C)
positive done
clear
D)
None of these done
clear
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question_answer16)
A particle starts with S.H.M. from the mean position as shown in figure below. Its amplitude is A and its time period is T. At one time, its speed is half that of the maximum speed. What is the displacement at that time?
A)
\[\frac{\sqrt{2}A}{3}\] done
clear
B)
\[\frac{\sqrt{3}A}{2}\] done
clear
C)
\[\frac{2A}{\sqrt{3}}\] done
clear
D)
\[\frac{3A}{\sqrt{2}}\] done
clear
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question_answer17)
A body executing linear simple harmonic motion has a velocity of 3 m/s when its displacement is 4 cm and a velocity of 4 m/s when its displacement is 3 cm. What is the amplitude of oscillation?
A)
5 cm done
clear
B)
7.5 cm done
clear
C)
10 cm done
clear
D)
12.5 cm done
clear
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question_answer18)
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is \[10{{s}^{-1}}\]. At, t = 0 the displacement is 5 m. The initial phase is\[\frac{\pi }{4}\]. What is the maximum acceleration?
A)
\[500m/{{s}^{2}}\] done
clear
B)
\[500\,\sqrt{2}\,m/{{s}^{2}}\] done
clear
C)
\[750\,\,m/{{s}^{2}}\] done
clear
D)
\[750\,\sqrt{2}\,m/{{s}^{2}}\] done
clear
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question_answer19)
The displacement of a particle in SHM is\[x=10\sin \left( 2t-\frac{\pi }{6} \right)\] metre. When its displacement is 6 m, the velocity of the particle (in m s~1) is
A)
8 done
clear
B)
24 done
clear
C)
16 done
clear
D)
10 done
clear
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question_answer20)
Two particles are executing simple harmonic motion of the same amplitude A and frequency \[\omega \] along the x-axis. Their mean position is separated by distance\[{{X}_{0}}({{X}_{0}}>A)\]. If the maximum separation between them is \[({{X}_{0}}+A)\], the phase difference between their motion is
A)
\[\frac{\pi }{3}\] done
clear
B)
\[\frac{\pi }{4}\] done
clear
C)
\[\frac{\pi }{6}\] done
clear
D)
\[\frac{\pi }{2}\] done
clear
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question_answer21)
A graph of the square of the velocity against the square of the acceleration of a given simple harmonic motion is
A)
B)
C)
D)
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question_answer22)
For a particle moving according to the equation \[x=a\,\cos \,\pi \,t\], the displacement in 3 s is
A)
0 done
clear
B)
0.5a done
clear
C)
1.5a done
clear
D)
2a done
clear
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question_answer23)
A body oscillates with SHM according to the equation (in SI units), \[x=5\,\cos \,\left( 2\pi t\frac{\pi }{4} \right)\]. Its instantaneous displacement at t = 1 second is
A)
\[\frac{\sqrt{2}}{5}m\] done
clear
B)
\[\frac{1}{\sqrt{3}}m\] done
clear
C)
\[\frac{5}{\sqrt{2}}m\] done
clear
D)
\[\frac{1}{2}m\] done
clear
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question_answer24)
A point mass oscillates along the x-axis according to the law\[x={{x}_{0}}\cos (\omega t-\pi /4)\]. If the acceleration of the particle is written as \[a=A\,\cos (\omega t+\delta )\], then
A)
\[A={{x}_{0}}{{\omega }^{2}},\,\delta =3\pi /4\] done
clear
B)
\[A={{x}_{0}},\,\delta =-\pi /4\] done
clear
C)
\[A={{x}_{0}}{{\omega }^{2}},\,\delta =\pi /4\] done
clear
D)
\[A={{x}_{0}}{{\omega }^{2}},\,\delta =-\pi /4\] done
clear
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question_answer25)
The displacement vs time of a particle executing SHM is shown in figure. The initial phase \[\phi \] is
A)
\[-\pi <\phi <-\frac{\pi }{2}\] done
clear
B)
\[\pi <\phi <\frac{3\pi }{2}\] done
clear
C)
\[-\frac{3\pi }{2}<\phi <-\pi \] done
clear
D)
\[\frac{\pi }{2}<\phi <\pi \] done
clear
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question_answer26)
The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes \[8\sqrt{3}\,cm/s\], will be
A)
\[2\sqrt{3\,}cm\] done
clear
B)
\[\sqrt{3\,}cm\] done
clear
C)
1cm done
clear
D)
2cm done
clear
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question_answer27)
Two simple harmonic motions are represented by the equations \[{{y}_{1}}=0.1\sin \left( 100\pi t+\frac{\pi }{3} \right)\]and \[{{y}_{2}}=0.1\cos \pi t\]. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is
A)
\[\frac{\pi }{3}\] done
clear
B)
\[\frac{-\pi }{6}\] done
clear
C)
\[\frac{\pi }{6}\] done
clear
D)
\[\frac{-\pi }{3}\] done
clear
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question_answer28)
Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference
A)
0 done
clear
B)
\[2\pi /3\] done
clear
C)
\[\pi \] done
clear
D)
\[\pi /6\] done
clear
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question_answer29)
A particle executs SHM with time period 8 s. Initially, it is at its mean position. The ratio of distance travelled by it in the 1st second to that in the 2nd second is
A)
\[\sqrt{2}:1\] done
clear
B)
\[1:(\sqrt{2}-1)\] done
clear
C)
\[(\sqrt{2}+1):\sqrt{2}\] done
clear
D)
\[(\sqrt{2}-1):1\] done
clear
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question_answer30)
The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t = 4 / 3 s is
A)
\[\frac{\sqrt{3}}{32}{{\pi }^{2}}cm/{{s}^{2}}\] done
clear
B)
\[\frac{-{{\pi }^{2}}}{32}cm/{{s}^{2}}\] done
clear
C)
\[\frac{{{\pi }^{2}}}{32}cm/{{s}^{2}}\] done
clear
D)
\[-\frac{\sqrt{3}}{32}{{\pi }^{2}}cm/{{s}^{2}}\] done
clear
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question_answer31)
A particle executing SHM has velocities u and v and acceleration a and b in two of its positions. Find the distance between these two positions.
A)
\[\frac{{{u}^{2}}+{{v}^{2}}}{a+b}\] done
clear
B)
\[\frac{{{v}^{2}}+{{u}^{2}}}{a-b}\] done
clear
C)
\[\frac{{{v}^{2}}+{{u}^{2}}}{a+b}\] done
clear
D)
\[\frac{{{v}^{2}}-{{u}^{2}}}{a-b}\] done
clear
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question_answer32)
A particle executing harmonic motion is having velocities \[{{v}_{1}}\] and \[{{v}_{2}}\] at distances is x, and x, from the equilibrium position. The amplitude of the motion is
A)
\[\sqrt{\frac{v_{1}^{2}{{x}_{2}}-v_{2}^{2}{{x}_{1}}}{v_{1}^{2}+v_{2}^{2}}}\] done
clear
B)
\[\sqrt{\frac{v_{1}^{2}x_{1}^{2}-v_{2}^{2}x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}\] done
clear
C)
\[\sqrt{\frac{v_{1}^{2}x_{2}^{2}-v_{2}^{2}x_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}}\] done
clear
D)
\[\sqrt{\frac{v_{1}^{2}x_{2}^{2}+v_{2}^{2}x_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}}\] done
clear
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question_answer33)
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency co. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
A)
at the mean position of the platform done
clear
B)
for an amplitude of \[\frac{g}{{{\omega }^{2}}}\] done
clear
C)
for an amplitude of\[\frac{g}{{{\omega }^{2}}}\] done
clear
D)
at the highest position of the platform done
clear
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question_answer34)
Two simple harmonic motions of angular frequency 100 and 1000 r\[rad\,{{s}^{-1}}\]have the same displacement amplitude. The ratio of their maximum accelerations is:
A)
1:10 done
clear
B)
\[1:{{10}^{2}}\] done
clear
C)
\[1:{{10}^{3}}\] done
clear
D)
\[1:{{10}^{4}}\] done
clear
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question_answer35)
Two particles execute SHM on same straight line with same mean position, same time period 6 second and same amplitude 5cm. Both the particles start SHM from their mean position (in same direction) with a time gap of 1 second. The maximum separation between the two particles during their motion is
A)
2cm done
clear
B)
3cm done
clear
C)
4cm done
clear
D)
5cm done
clear
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question_answer36)
A particle is executing simple harmonic motion with amplitude A. When the ratio of its kinetic energy to the potential energy is\[\frac{1}{4}\], its displacement from its mean position is
A)
\[\frac{2}{\sqrt{5}}A\] done
clear
B)
\[\frac{\sqrt{3}}{2}A\] done
clear
C)
\[\frac{3}{4}A\] done
clear
D)
\[\frac{1}{4}A\] done
clear
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question_answer37)
A mass of 4 kg suspended from a spring of force constant 800 N m~1 executes simple harmonic oscillations. If the total energy of the oscillator is 4 J, the maximum acceleration (\[in\,m\,{{s}^{-2}}\]) of the mass is
A)
5 done
clear
B)
15 done
clear
C)
45 done
clear
D)
20 done
clear
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question_answer38)
A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function of displacement x. Which of the following statement is true?
A)
P.E. is maximum when x = 0. done
clear
B)
K.E. is maximum when x = 0. done
clear
C)
T. E. is zero when x = 0. done
clear
D)
K.E. is maximum when x is maximum. done
clear
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question_answer39)
If< E > and < U> denote the average kinetic and the average potential energies respectively of mass describing a simple harmonic motion, over one period, then the correct relation is
A)
<E>=<U> done
clear
B)
<E>=2<U> done
clear
C)
<E>=-2<U> done
clear
D)
<E>=-< U> done
clear
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question_answer40)
What do you conclude from the graph about the frequency of KE, PE and SHM?
A)
Frequency of KE and PE is double the frequency of SHM. done
clear
B)
Frequency of KE and PE is four times the frequency SHM. done
clear
C)
Frequency of PE is double the frequency of K.E. done
clear
D)
Frequency of KE and PE is equal to the frequency of SHM. done
clear
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question_answer41)
A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is
A)
\[2{{\pi }^{2}}m{{a}^{2}}{{v}^{2}}\] done
clear
B)
\[{{\pi }^{2}}m{{a}^{2}}{{v}^{2}}\] done
clear
C)
\[\frac{1}{4}m{{a}^{2}}{{v}^{2}}\] done
clear
D)
\[4{{\pi }^{2}}m{{a}^{2}}{{v}^{2}}\] done
clear
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question_answer42)
A particle of mass m is executing oscillations about the origin on the X-axis with amplitude A. Its potential energy is given as \[U(x)=\alpha {{x}^{4}}\] where a is a positive constant. The x coordinate of the particle where the potential energy is one third of the kinetic energy is
A)
\[\pm A/2\] done
clear
B)
\[\pm A/\sqrt{2}\] done
clear
C)
\[\pm A/3\] done
clear
D)
\[\pm A/\sqrt{3}\] done
clear
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question_answer43)
A particle of mass 10 gm is describing S.H. M. along a straight line with period of 2 sec and amplitude of 10 cm. Its kinetic energy when it is at 5 cm from its equilibrium position is
A)
\[37.5{{\pi }^{2}}\,ergs\] done
clear
B)
\[3.75{{\pi }^{2}}\,ergs\] done
clear
C)
\[375{{\pi }^{2}}\,ergs\] done
clear
D)
\[0.375{{\pi }^{2}}\,erg\] done
clear
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question_answer44)
A particle of mass 1 kg is placed in a potential field. Its potential energy is given by \[U=10{{x}^{2}}+5\].The frequency of oscillations of the particle is given by
A)
\[(\sqrt{10})\] done
clear
B)
\[(\sqrt{5})\] done
clear
C)
\[\left( \sqrt{\frac{10}{\pi }} \right)\] done
clear
D)
\[\left( \frac{\sqrt{5}}{\pi } \right)\] done
clear
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question_answer45)
A body is executing simple harmonic motion. At a displacement x from mean position, its potential energy is \[{{E}_{1}}=2J\] and at a displacement y from mean position, its potential energy is\[{{E}_{2}}=8J\]. The potential energy E at a displacement (x + y) from mean position is
A)
10J done
clear
B)
14J done
clear
C)
18J done
clear
D)
4J done
clear
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question_answer46)
The particle executing simple harmonic motion has a kinetic energy\[{{K}_{0}}{{\cos }^{2}}\omega t\]. The maximum values of the potential energy and the total energy are respectively
A)
\[{{K}_{0}}/2\,and\,{{K}_{0}}\] done
clear
B)
\[{{K}_{0}}\,and\,2{{K}_{0}}\] done
clear
C)
\[{{K}_{0}}\,and\,{{K}_{0}}\] done
clear
D)
\[0\,and\,2{{K}_{0}}\] done
clear
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question_answer47)
A particle of mass m oscillates with simple harmonic motion between points \[{{x}_{1}}\] and \[{{x}_{2}}\], the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph.
A)
B)
C)
D)
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question_answer48)
A linear harmonic oscillator of force constant \[2\times {{10}^{6}}N/m\] and amplitude 0.01 m has a total mechanical energy of 160 J. Its
A)
potential energy is 160 J done
clear
B)
potential energy is 100 J done
clear
C)
potential energy is zero done
clear
D)
potential energy is 120 J done
clear
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question_answer49)
The angular velocity and the amplitude of a simple pendulum is o and a respectively. At a displacement x from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to Vis
A)
\[\frac{({{a}^{2}}-{{x}^{2}}{{\omega }^{2}})}{{{x}^{2}}{{\omega }^{2}}}\] done
clear
B)
\[\frac{{{x}^{2}}{{\omega }^{2}}}{({{a}^{2}}-{{x}^{2}}{{\omega }^{2}})}\] done
clear
C)
\[\frac{({{a}^{2}}-{{x}^{2}})}{{{x}^{2}}}\] done
clear
D)
\[\frac{{{x}^{2}}}{({{a}^{2}}-{{x}^{2}})}\] done
clear
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question_answer50)
A simple pendulum oscillates in air with time period T and amplitude A. As the time passes
A)
T and A both decrease done
clear
B)
T increases and A is constant done
clear
C)
T remains same and A decreases done
clear
D)
T decreases and A is constant done
clear
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question_answer51)
If the maximum velocity and acceleration of a particle executing SHM are equal in magnitude, the time period will be
A)
1.57 sec done
clear
B)
3.14 sec done
clear
C)
6.28 sec done
clear
D)
12.56 sec done
clear
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question_answer52)
A particle executes simple harmonic motion between \[x=-A\] and \[x=+A\]. The time taken for it to go from O to A/2 is \[{{T}_{1}}\] and\[{{T}_{1}}\] and to go from A/2 to A is \[{{T}_{2}}\]. Then
A)
\[{{T}_{1}}<{{T}_{2}}\] done
clear
B)
\[{{T}_{1}}>{{T}_{2}}\] done
clear
C)
\[{{T}_{1}}={{T}_{2}}\] done
clear
D)
\[{{T}_{1}}=2{{T}_{2}}\] done
clear
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question_answer53)
If a particle takes 0.5 sec to reach position of minimum velocity from previous such position, then
A)
\[T=6\sec ,\,v=1/6\,Hz\] done
clear
B)
\[T=2\sec ,\,v=1\,Hz\] done
clear
C)
\[T=3\sec ,\,v=3\,Hz\] done
clear
D)
\[T=1\sec ,\,v=1\,Hz\] done
clear
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question_answer54)
A simple harmonic motion has an amplitude A and time period T. The time required by it to travel from x=A to x=A/2 is
A)
T/6 done
clear
B)
T/4 done
clear
C)
T/3 done
clear
D)
T/2 done
clear
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question_answer55)
Frequency of oscillation is proportional to
A)
\[\sqrt{\frac{3k}{m}}\] done
clear
B)
\[\sqrt{\frac{k}{m}}\] done
clear
C)
\[\sqrt{\frac{2k}{m}}\] done
clear
D)
\[\sqrt{\frac{m}{3k}}\] done
clear
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question_answer56)
The bob of a simple pendulum of mass m and total energy E will have maximum linear momentum equal to
A)
\[\sqrt{\frac{2E}{m}}\] done
clear
B)
\[\sqrt{2mE}\] done
clear
C)
\[2mE\] done
clear
D)
\[m{{E}^{2}}\] done
clear
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question_answer57)
A particle executing simple harmonic motion covers a distance equal to half of its amplitude in one second. Then the time period of the simple harmonic motion is
A)
4s done
clear
B)
6s done
clear
C)
8s done
clear
D)
12s done
clear
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question_answer58)
The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is
A)
0.01s done
clear
B)
10s done
clear
C)
0.ls done
clear
D)
100s done
clear
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question_answer59)
A body is executing S.H.M. When its displacement from the mean position are 4 cm and 5 cm, it has velocities \[10cm\,{{s}^{-1}}\] and \[8\,cm\,{{s}^{-1}}\] respectively. Its periodic time is
A)
\[\pi /2\,s\] done
clear
B)
\[\pi s\] done
clear
C)
\[3\pi /2s\] done
clear
D)
\[2\pi s\] done
clear
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question_answer60)
The displacement of an object "attached to a spring and executing simple harmonic motion is given by \[x=2\times {{10}^{-2\,\,\,}}\cos \,\pi t\] metre. The time at which the maximum speed first occurs is
A)
0.25s done
clear
B)
0.5s done
clear
C)
0.75s done
clear
D)
0.125s done
clear
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question_answer61)
A particle at the end of a spring executes S.H.M with a period\[{{t}_{1}}\], while the corresponding period for another spring is \[{{t}_{2}}\]. If the period of oscillation with the two springs in series is T then
A)
\[{{T}^{-1}}={{t}_{1}}^{-1}+{{t}_{2}}^{-1}\] done
clear
B)
\[{{T}^{2}}=t_{1}^{2}+t_{2}^{2}\] done
clear
C)
\[T={{t}_{1}}+{{t}_{2}}\] done
clear
D)
\[{{T}^{-2}}=t_{1}^{-2}+t_{2}^{-2}\] done
clear
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question_answer62)
A particle is executing SHM along a straight line. Its velocities at distances \[{{x}_{1}}\]and \[{{x}_{2}}\]from the mean position are \[{{V}_{1}}\]and\[{{V}_{2}}\], respectively. Its time period is
A)
\[2\pi \sqrt{\frac{x_{2}^{2}-x_{1}^{2}}{V_{1}^{2}-V_{2}^{2}}}\] done
clear
B)
\[2\pi \sqrt{\frac{V_{1}^{2}+V_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}\] done
clear
C)
\[2\pi \sqrt{\frac{V_{1}^{2}-V_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}\] done
clear
D)
\[2\pi \sqrt{\frac{x_{1}^{2}-x_{2}^{2}}{V_{1}^{2}-V_{2}^{2}}}\] done
clear
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question_answer63)
A simple harmonic wave having an amplitude a and time period T is represented by the equation\[y=5\sin \pi (t+4)m\]. Then the value of amplitude in (m) and time period (T) in second are
A)
\[a=10,\,T=2\] done
clear
B)
a=5,T=l done
clear
C)
a=10,T=l done
clear
D)
a=5,T=2 done
clear
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question_answer64)
What will be the force constant of the spring system shown in figure?
A)
\[\frac{{{k}_{1}}}{2}+{{k}_{2}}\] done
clear
B)
\[{{\left[ \frac{1}{2{{k}_{1}}}+\frac{1}{{{k}_{2}}} \right]}^{-1}}\] done
clear
C)
\[\left[ \frac{1}{2{{k}_{1}}}+\frac{1}{{{k}_{2}}} \right]\] done
clear
D)
\[{{\left[ \frac{2}{{{k}_{1}}}+\frac{1}{{{k}_{2}}} \right]}^{-1}}\] done
clear
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question_answer65)
A particle of mass m oscillates with a potential energy\[U={{U}_{0}}+\alpha \,\,{{x}^{2}}\], where \[{{U}_{0}}\] and a are constants and x is the displacement of particle from equilibrium position. The time period of oscillation is
A)
\[2\pi \sqrt{\frac{m}{\alpha }}\] done
clear
B)
\[2\pi \sqrt{\frac{m}{2\alpha }}\] done
clear
C)
\[\pi \sqrt{\frac{2m}{\alpha }}\] done
clear
D)
\[2\pi \sqrt{\frac{m}{{{\alpha }^{2}}}}\] done
clear
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question_answer66)
The average value of potential energy for one complete oscillation cycle of a body of mass m executing S.H.M. having angular frequency \[\omega \] and maximum amplitude a is given by:
A)
\[\frac{1}{2}m{{\omega }^{2}}{{a}^{2}}\] done
clear
B)
\[\frac{1}{4}m{{\omega }^{2}}{{a}^{2}}\] done
clear
C)
\[\frac{1}{8}m{{\omega }^{2}}{{a}^{2}}\] done
clear
D)
\[\frac{1}{16}m{{\omega }^{2}}{{a}^{2}}\] done
clear
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question_answer67)
A wall clock uses a vertical spring-mass system to measure the time. Each time the mass reaches an extreme position, the clock advances by a second. The clock gives correct time at the equator. If the clock is taken to the poles it will
A)
run slow done
clear
B)
run fast done
clear
C)
stop working done
clear
D)
give correct time done
clear
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question_answer68)
The height of liquid column in a U tube is 0.3 m. If the liquid in one of the limbs is depressed and then released, then the time period of the liquid column will be
A)
1.1 sec done
clear
B)
19 sec done
clear
C)
0.11 sec done
clear
D)
2 sec done
clear
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question_answer69)
A block rests on a horizontal table which is executing SHM in the horizontal plane with an amplitude 'a'. If the coefficient of friction is \['\mu '\], then the block just starts to slip when the frequency of oscillation is
A)
\[\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}\] done
clear
B)
\[\sqrt{\frac{\mu g}{a}}\] done
clear
C)
\[2\pi \sqrt{\frac{a}{\mu g}}\] done
clear
D)
\[\sqrt{\frac{a}{\mu g}}\] done
clear
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question_answer70)
On earth, a body suspended on a spring of negligible mass causes extension L and undergoes oscillations along length of the spring with frequency f. On the Moon, the same quantities are L/n and f respectively. The ratio f?/f is
A)
n done
clear
B)
\[\frac{1}{n}\] done
clear
C)
\[{{n}^{-1/2}}\] done
clear
D)
1 done
clear
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question_answer71)
A second's pendulum is placed in a space laboratory orbiting around the earth at a height 3 R from the earth's surface where R is earth's radius. The time period of the pendulum will be
A)
zero done
clear
B)
\[2\sqrt{3}\] done
clear
C)
4 sec done
clear
D)
infinite done
clear
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question_answer72)
A bent tube of uniform cross-section area A has a non-viscous liquid of density p. The mass of liquid in the tube is m. The time period of oscillation of the liquid is
A)
\[2\pi \sqrt{\frac{m}{\rho gA}}\] done
clear
B)
\[2\pi \sqrt{\frac{m}{2\rho gA}}\] done
clear
C)
\[2\pi \sqrt{\frac{2m}{\rho gA}}\] done
clear
D)
None of these done
clear
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question_answer73)
A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to\[{{T}_{M}}\]. If the Young's modulus of the material of the wire is Y then\[\frac{1}{Y}\] is equal to: (g = gravitational acceleration)
A)
\[\left[ 1-{{\left( \frac{{{T}_{M}}}{T} \right)}^{2}} \right]\frac{A}{Mg}\] done
clear
B)
\[\left[ 1-{{\left( \frac{T}{{{T}_{M}}} \right)}^{2}} \right]\frac{A}{Mg}\] done
clear
C)
\[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{A}{Mg}\] done
clear
D)
\[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{Mg}{A}\] done
clear
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question_answer74)
Masses \[{{M}_{A}}\] and \[{{M}_{B}}\] hanging from the ends of strings of lengths \[{{L}_{A}}\] and \[{{L}_{B}}\] are executing simple harmonic- motions. If their frequencies are \[{{f}_{A}}=2{{f}_{B}}\], then
A)
\[{{L}_{A}}=2{{L}_{B}}\,and\,{{M}_{A}}={{M}_{B}}/2\] done
clear
B)
\[{{L}_{A}}=4{{L}_{B}}\] regardless of masses done
clear
C)
\[{{L}_{A}}={{L}_{B}}/4\] regardless of masses done
clear
D)
\[{{L}_{A}}=2{{L}_{B}}\,\,\,and\,{{M}_{A}}=2{{M}_{B}}\] done
clear
View Solution play_arrow
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question_answer75)
A simple pendulum has time period\[{{T}_{1}}\]. The point of suspension is now moved upward according to the relation \[y=K{{t}^{2}},(K=1m/{{s}^{2}})\] where y is the vertical displacement. The time period now becomes\[{{T}_{2}}\]. The ratio of \[\frac{T_{1}^{2}}{T_{2}^{2}}\] is \[(g=10m/{{s}^{2}})\]
A)
5/6 done
clear
B)
6/5 done
clear
C)
1 done
clear
D)
4/5 done
clear
View Solution play_arrow
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question_answer76)
A cylindrical block of wood (density = 650 kg \[{{m}^{-3}}\]), of base area 30cm2 and height 54 cm, floats in a liquid of density 900 kg \[{{m}^{-3}}\]. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly)
A)
52cm done
clear
B)
65cm done
clear
C)
39cm done
clear
D)
26cm done
clear
View Solution play_arrow
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question_answer77)
A body executes simple harmonic motion under the action of a force \[{{F}_{1}}\] with a time period \[\frac{4}{5}\]s. If the force is changed to\[{{F}_{2}}\], it executes S.H.M. with time period - s. If both the forces \[{{F}_{1}}\] and \[{{F}_{2}}\] act simultaneously in the same direction on the body, its time period in second is
A)
\[\frac{12}{25}\] done
clear
B)
\[\frac{7}{5}\] done
clear
C)
\[\frac{24}{25}\] done
clear
D)
\[\frac{5}{7}\] done
clear
View Solution play_arrow
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question_answer78)
If the differential equation for a simple harmonic motion is \[\frac{{{d}^{2}}{{y}^{2}}}{d{{t}^{2}}}+2y=0\], the time-period of the motion is
A)
\[\pi \sqrt{2}s\] done
clear
B)
\[\frac{\sqrt{2}s}{\pi }\] done
clear
C)
\[\frac{\pi }{\sqrt{2}}\] done
clear
D)
\[2\pi s\] done
clear
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question_answer79)
Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal direction, then the frequency of the system is
A)
\[\frac{1}{2\pi }\sqrt{\frac{k}{4M}}\] done
clear
B)
\[\frac{1}{2\pi }\sqrt{\frac{4k}{M}}\] done
clear
C)
\[\frac{1}{2\pi }\sqrt{\frac{k}{7M}}\] done
clear
D)
\[\frac{1}{2\pi }\sqrt{\frac{7k}{M}}\] done
clear
View Solution play_arrow
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question_answer80)
The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is \[{{t}_{0}}\]in air. Neglecting frictional force of water and given that the density of the bob is\[(4/3)\times 1000kg/{{m}^{3}}\]. What relationship between t and \[{{t}_{0}}\] is true?
A)
\[t={{t}_{0}}\] done
clear
B)
\[t={{t}_{0}}/2\] done
clear
C)
\[t=2{{t}_{0}}\] done
clear
D)
\[t=4{{t}_{0}}\] done
clear
View Solution play_arrow
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question_answer81)
A U-tube is of non uniform cross-section. The area of cross-sections of two sides of tube are A and 2A (see fig.). It contains non-viscous liquid of mass m. The liquid is displaced slightly and free to oscillate. Its time period of oscillations is
A)
\[T=2\pi \sqrt{\frac{m}{3\rho gA}}\] done
clear
B)
\[T=2\pi \sqrt{\frac{m}{2\rho gA}}\] done
clear
C)
\[T=2\pi \sqrt{\frac{m}{\rho gA}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer82)
A small ball of density \[4{{\rho }_{0}}\] is released from rest just below the surface of a liquid. The density of liquid increases with depth as \[\rho ={{\rho }_{0}}(1+ay)\] where \[a=2{{m}^{-1}}\]is a constant. Find the time period of its oscillation. (Neglect the viscosity effects).
A)
\[\frac{2\pi }{\sqrt{5}}\sec \] done
clear
B)
\[\frac{\pi }{\sqrt{5}}\sec \] done
clear
C)
\[\frac{\pi }{2\sqrt{5}}\sec \] done
clear
D)
\[\frac{3\pi }{2\sqrt{5}}\sec \] done
clear
View Solution play_arrow
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question_answer83)
A rod of mass M and length L is hinged at its centre of mass so that it can rotate in a vertical plane. Two springs each of stiffness k are connected at its ends, as shown in the figure. The time period of SHM is
A)
\[2\pi \sqrt{\frac{M}{6k}}\] done
clear
B)
\[2\pi \sqrt{\frac{M}{3k}}\] done
clear
C)
\[2\pi \sqrt{\frac{ML}{k}}\] done
clear
D)
\[\pi \sqrt{\frac{M}{6k}}\] done
clear
View Solution play_arrow
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question_answer84)
Disregarding gravity, find the period of oscillation of the particle connected with four springs as shown in the figure. (Given:\[\theta ={{45}^{o}},\beta ={{30}^{o}}\])
A)
\[\pi \sqrt{\frac{2m}{k}}\] done
clear
B)
\[\sqrt{\frac{2m\pi }{k}}\] done
clear
C)
\[\sqrt{\frac{m\pi }{2k}}\] done
clear
D)
\[\pi \sqrt{\frac{m}{2k}}\] done
clear
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question_answer85)
Two springs, each of spring constant\[k=100N/m\], are attached to a block of mass 2 kg as shown in the figure. The block can slide smoothly along a horizontal platform clamped to the opposite walls of the trolley of mass 5kg. If the block is displaced by x cm. and released, the period of oscillation in seconds is
A)
\[T=2\pi \sqrt{\frac{1}{20}}\] done
clear
B)
\[T=2\pi \sqrt{\frac{7}{1000}}\] done
clear
C)
\[T=2\pi \sqrt{\frac{1}{140}}\] done
clear
D)
\[T=2\pi \frac{49}{100}\] done
clear
View Solution play_arrow
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question_answer86)
If a body oscillates at the angular frequency \[{{\omega }_{d}}\] of the driving force, then the oscillations are called
A)
free oscillations done
clear
B)
coupled oscillations done
clear
C)
forced oscillations done
clear
D)
maintained oscillations done
clear
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question_answer87)
In case of a forced vibration, the resonance wave becomes very sharp when the
A)
quality factor is small done
clear
B)
damping force is small done
clear
C)
restoring force is small done
clear
D)
applied periodic force is small done
clear
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question_answer88)
When an oscillator completes 100 oscillations its amplitude reduces to\[\frac{1}{3}\] of its initial value. What will be its amplitude, when it complete 200 oscillations?
A)
\[\frac{1}{8}\] done
clear
B)
\[\frac{2}{3}\] done
clear
C)
\[\frac{1}{6}\] done
clear
D)
\[\frac{1}{9}\] done
clear
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question_answer89)
A forced oscillator is acted upon by a force \[F={{F}_{0}}\] sin cot. The amplitude of oscillation is given by \[\frac{55}{\sqrt{2{{\omega }^{2}}-36\omega +9}}\]. The resonant angular frequency is
A)
2 unit done
clear
B)
9 unit done
clear
C)
18 unit done
clear
D)
36 unit done
clear
View Solution play_arrow
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question_answer90)
A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force F sin\[\omega t\]. If the amplitude of the particle is maximum for \[\omega ={{\omega }_{1}}\] and the energy of the particle is maximum for \[\omega ={{\omega }_{2}}\], then
A)
\[{{\omega }_{1}}={{\omega }_{2}}\,and\,{{\omega }_{2}}\ne {{\omega }_{0}}\] done
clear
B)
\[{{\omega }_{1}}={{\omega }_{0}}\,and\,{{\omega }_{2}}={{\omega }_{0}}\] done
clear
C)
\[{{\omega }_{1}}\ne {{\omega }_{0}}\,and\,{{\omega }_{2}}={{\omega }_{0}}\] done
clear
D)
\[{{\omega }_{1}}\ne {{\omega }_{0}}\,and\,{{\omega }_{2}}\ne {{\omega }_{0}}\] done
clear
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question_answer91)
A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency\[{{\omega }_{0}}\]. An external force F (t) proportional to \[\cos \,\omega t(\omega \ne {{\omega }_{0}})\] is applied to the oscillator. The displacement of the oscillator will be proportional to
A)
\[\frac{1}{m(\omega _{0}^{2}+{{\omega }^{2}})}\] done
clear
B)
\[\frac{1}{m(\omega _{0}^{2}-{{\omega }^{2}})}\] done
clear
C)
\[\frac{m}{\omega _{0}^{2}-{{\omega }^{2}}}\] done
clear
D)
\[\frac{m}{(\omega _{0}^{2}+{{\omega }^{2}})}\] done
clear
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question_answer92)
What is the amplitude of simple harmonic motion at resonance in the ideal case of zero damping?
A)
Zero done
clear
B)
-1 done
clear
C)
1 done
clear
D)
Infinite done
clear
View Solution play_arrow
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question_answer93)
If a simple pendulum has significant amplitude (upto a factor of \[1/e\] of original) only in the period between \[t=0s\,to\,t=\tau s\], then \[\tau \] may be called the average life of the pendulum, when the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with b as the constant of proportionality, the average life time of the pendulum is (assuming damping the small) in seconds
A)
\[\frac{0.693}{b}\] done
clear
B)
b done
clear
C)
\[\frac{1}{b}\] done
clear
D)
\[\frac{2}{b}\] done
clear
View Solution play_arrow
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question_answer94)
A pendulum with time period of 1s is losing energy. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in s~1) is :
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{30}\] done
clear
C)
2 done
clear
D)
\[\frac{1}{15}In\,3\] done
clear
View Solution play_arrow
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question_answer95)
In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value \[{{a}_{0}}\] at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be
A)
\[{{a}_{0}}/2\] done
clear
B)
\[{{a}_{0}}/4\] done
clear
C)
\[{{a}_{0}}/6\] done
clear
D)
\[{{a}_{0}}/9\] done
clear
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question_answer96)
A block connected to a spring oscillates vertically. A damping force\[{{F}_{d}}\] , acts on the block by the surrounding medium. Given as \[{{F}_{d}}=-bVb\] is a positive constant which depends on :
A)
viscosity of the medium done
clear
B)
size of the block done
clear
C)
shape of the block done
clear
D)
All of these done
clear
View Solution play_arrow
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question_answer97)
The amplitude of a damped oscillator becomes\[{{\left( \frac{1}{3} \right)}^{rd}}\] in 2 seconds. If its amplitude after 6 seconds is\[\frac{1}{n}\] times the original amplitude, the value of n is
A)
\[{{3}^{2}}\] done
clear
B)
\[{{3}^{3}}\] done
clear
C)
\[\sqrt[3]{3}\] done
clear
D)
\[{{2}^{3}}\] done
clear
View Solution play_arrow
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question_answer98)
In case of sustained forced oscillations the amplitude of oscillations
A)
decreases linearly done
clear
B)
decreases sinusoidally done
clear
C)
decreases exponentially done
clear
D)
always remains constant done
clear
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question_answer99)
The amplitude of velocity of a particle is given by, \[{{V}_{m}}={{V}_{0}}/(a{{\omega }^{2}}-b\omega +c)\] where \[{{V}_{0}}\], a, b and c are positive: The condition for a single resonant frequency is
A)
\[{{b}^{2}}<4ac\] done
clear
B)
\[{{b}^{2}}=4ac\] done
clear
C)
\[{{b}^{2}}=5ac\] done
clear
D)
\[{{b}^{2}}=7ac\] done
clear
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question_answer100)
The time period of simple pendulum of length 1m suspended in a car that is moving with constant speed 36 km/hr around a circle of radius 10mis:
A)
\[\pi \sqrt{2}\sec \] done
clear
B)
\[\frac{\pi }{10}\sqrt{2}\sec \] done
clear
C)
\[\frac{\pi }{10\sqrt{2}}\sec \] done
clear
D)
\[\frac{5\pi }{\sqrt{2}}\sec \] done
clear
View Solution play_arrow