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question_answer1)
A simple pendulum performs simple harmonic motion about X = 0 with an amplitude A and time period T. The speed of the pendulum at \[X=\frac{A}{2}\] will be [MP PMT 1987]
A)
\[\frac{\pi A\sqrt{3}}{T}\] done
clear
B)
\[\frac{\pi A}{T}\] done
clear
C)
\[\frac{\pi A\sqrt{3}}{2T}\] done
clear
D)
\[\frac{3{{\pi }^{2}}A}{T}\] done
clear
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question_answer2)
A body is executing simple harmonic motion with an angular frequency \[2rad/s\]. The velocity of the body at 20 mm displacement, when the amplitude of motion is 60 mm, is [Pb. CET 1996; Pb. PMT 1997; AFMC 1998; CPMT 1999]
A)
40 mm /s done
clear
B)
\[60mm/s\] done
clear
C)
\[113mm/s\] done
clear
D)
\[120mm/s\] done
clear
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question_answer3)
A body of mass 5 gm is executing S.H.M. about a point with amplitude 10 cm. Its maximum velocity is 100 cm/sec. Its velocity will be 50 cm/sec at a distance [CPMT 1976]
A)
5 done
clear
B)
\[5\sqrt{2}\] done
clear
C)
\[5\sqrt{3}\] done
clear
D)
\[10\sqrt{2}\] done
clear
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question_answer4)
A simple harmonic oscillator has a period of 0.01 sec and an amplitude of 0.2 m. The magnitude of the velocity in \[m{{\sec }^{-1}}\] at the centre of oscillation is [JIPMER 1997]
A)
\[20\pi \] done
clear
B)
100 done
clear
C)
40p done
clear
D)
\[100\pi \] done
clear
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question_answer5)
A particle executes S.H.M. with a period of 6 second and amplitude of 3 cm. Its maximum speed in cm/sec is [AIIMS 1982]
A)
\[\pi /2\] done
clear
B)
\[\pi \] done
clear
C)
\[2\pi \] done
clear
D)
\[3\pi \] done
clear
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question_answer6)
A particle is executing S.H.M. If its amplitude is 2 m and periodic time 2 seconds, then the maximum velocity of the particle will be [MP PMT 1985]
A)
\[\pi \,m/s\] done
clear
B)
\[\sqrt{2\pi }\,m/s\] done
clear
C)
\[2\pi \,m/s\] done
clear
D)
\[4\pi \,m/s\] done
clear
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question_answer7)
A S.H.M. has amplitude ?a? and time period T. The maximum velocity will be [MP PMT 1985; CPMT 1997; UPSEAT 1999]
A)
\[\frac{4a}{T}\] done
clear
B)
\[\frac{2a}{T}\] done
clear
C)
\[2\pi \sqrt{\frac{a}{T}}\] done
clear
D)
\[\frac{2\pi a}{T}\] done
clear
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question_answer8)
A body is executing S.H.M. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is [CPMT 1991; MP PET 1995]
A)
\[2\pi \,sec\] done
clear
B)
\[\pi /2\]sec done
clear
C)
\[\pi \,sec\] done
clear
D)
\[3\pi /2\,sec\] done
clear
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question_answer9)
A particle has simple harmonic motion. The equation of its motion is \[x=5\sin \left( 4t-\frac{\pi }{6} \right)\], where x is its displacement. If the displacement of the particle is 3 units, then it velocity is [MP PMT 1994]
A)
\[\frac{2\pi }{3}\] done
clear
B)
\[\frac{5\pi }{6}\] done
clear
C)
\[20\] done
clear
D)
\[16\] done
clear
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question_answer10)
If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 sec, then its maximum velocity is [AIIMS 1998; MH CET 2000; DPMT 2000]
A)
0.10 m / s done
clear
B)
0.15 m / s done
clear
C)
0.8 m / s done
clear
D)
0.26 m / s done
clear
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question_answer11)
If the displacement of a particle executing SHM is given by \[y=0.30\sin (220t+0.64)\] in metre, then the frequency and maximum velocity of the particle is [AFMC 1998]
A)
35 Hz, 66 m / s done
clear
B)
45 Hz, 66 m / s done
clear
C)
58 Hz, 113 m / s done
clear
D)
35 Hz, 132 m / s done
clear
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question_answer12)
The maximum velocity and the maximum acceleration of a body moving in a simple harmonic oscillator are \[2\,m/s\] and \[4\,m/{{s}^{2}}.\] Then angular velocity will be [Pb. PMT 1998; MH CET 1999, 2003]
A)
3 rad/sec done
clear
B)
0.5 rad/sec done
clear
C)
1 rad/sec done
clear
D)
2 rad/sec done
clear
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question_answer13)
If a particle under S.H.M. has time period 0.1 sec and amplitude \[{{\tan }^{-1}}\frac{a}{g}\]. It has maximum velocity [RPET 2000]
A)
\[\frac{\pi }{25}\,m/s\] done
clear
B)
\[\frac{\pi }{26}\,m/s\] done
clear
C)
\[{{\tan }^{-1}}\frac{a}{g}\] done
clear
D)
None of these done
clear
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question_answer14)
A particle executing simple harmonic motion has an amplitude of 6 cm. Its acceleration at a distance of 2 cm from the mean position is \[8\,cm/{{s}^{2}}\]. The maximum speed of the particle is [EAMCET (Engg.) 2000]
A)
8 cm/s done
clear
B)
12 cm/s done
clear
C)
16 cm/s done
clear
D)
24 cm/s done
clear
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question_answer15)
A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean position the velocity of the particle is 10 cm/s. The distance of the particle from the mean position when its speed becomes 5 cm/s is [EAMCET (Med.) 2000]
A)
\[\sqrt{3}\,cm\] done
clear
B)
\[\sqrt{5}\,cm\] done
clear
C)
\[2(\sqrt{3})\,cm\] done
clear
D)
\[2(\sqrt{5})\,cm\] done
clear
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question_answer16)
Two particles P and Q start from origin and execute Simple Harmonic Motion along X-axis with same amplitude but with periods 3 seconds and 6 seconds respectively. The ratio of the velocities of P and Q when they meet is [EAMCET 2001]
A)
1 : 2 done
clear
B)
2 : 1 done
clear
C)
2 : 3 done
clear
D)
3 : 2 done
clear
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question_answer17)
A particle is performing simple harmonic motion with amplitude A and angular velocity w. The ratio of maximum velocity to maximum acceleration is [Kerala (Med.) 2002]
A)
w done
clear
B)
1/w done
clear
C)
w2 done
clear
D)
Aw done
clear
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question_answer18)
The angular velocities of three bodies in simple harmonic motion are \[{{\omega }_{1}},\,{{\omega }_{2}},\,{{\omega }_{3}}\] with their respective amplitudes as \[{{A}_{1}},\,{{A}_{2}},\,{{A}_{3}}\]. If all the three bodies have same mass and velocity, then [BHU 2002]
A)
\[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\] done
clear
B)
\[{{A}_{1}}{{\omega }_{1}}^{2}={{A}_{2}}{{\omega }_{2}}^{2}={{A}_{3}}{{\omega }_{3}}^{2}\] done
clear
C)
\[{{A}_{1}}^{2}{{\omega }_{1}}={{A}_{2}}^{2}{{\omega }_{2}}={{A}_{3}}^{2}{{\omega }_{3}}\] done
clear
D)
\[{{A}_{1}}^{2}{{\omega }_{1}}^{2}={{A}_{2}}^{2}{{\omega }_{2}}^{2}={{A}^{2}}\] done
clear
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question_answer19)
The velocity of a particle performing simple harmonic motion, when it passes through its mean position is [MH CET (Med.) 2002; BCECE 2004]
A)
Infinity done
clear
B)
Zero done
clear
C)
Minimum done
clear
D)
Maximum done
clear
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question_answer20)
The velocity of a particle in simple harmonic motion at displacement y from mean position is [BCECE 2003; RPMT 2003]
A)
\[\omega \sqrt{{{a}^{2}}+{{y}^{2}}}\] done
clear
B)
\[\omega \sqrt{{{a}^{2}}-{{y}^{2}}}\] done
clear
C)
\[\omega y\] done
clear
D)
\[{{\omega }^{2}}\sqrt{{{a}^{2}}-{{y}^{2}}}\] done
clear
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question_answer21)
A particle is executing the motion \[x=A\cos (\omega \,t-\theta )\]. The maximum velocity of the particle is [BHU 2003; CPMT 2004]
A)
\[A\omega \cos \theta \] done
clear
B)
\[A\omega \] done
clear
C)
\[A\omega \sin \theta \] done
clear
D)
None of these done
clear
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question_answer22)
A particle executing simple harmonic motion with amplitude of 0.1 m. At a certain instant when its displacement is 0.02 m, its acceleration is 0.5 m/s2. The maximum velocity of the particle is (in m/s) [MP PET 2003]
A)
0.01 done
clear
B)
0.05 done
clear
C)
0.5 done
clear
D)
0.25 done
clear
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question_answer23)
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 [Pb. PET 2003]
A)
\[2\sqrt{3}cm\] done
clear
B)
\[\sqrt{3}cm\] done
clear
C)
1 cm done
clear
D)
2 cm done
clear
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question_answer24)
The maximum velocity of a simple harmonic motion represented by \[y=3\sin \,\left( 100\,t+\frac{\pi }{6} \right)\]is given by [BCECE 2005]
A)
300 done
clear
B)
\[\frac{3\pi }{6}\] done
clear
C)
100 done
clear
D)
\[\frac{\pi }{6}\] done
clear
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question_answer25)
The displacement equation of a particle is \[x=3\sin 2t+4\cos 2t.\] The amplitude and maximum velocity will be respectively [RPMT 1998]
A)
5, 10 done
clear
B)
3, 2 done
clear
C)
4, 2 done
clear
D)
3, 4 done
clear
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question_answer26)
Velocity at mean position of a particle executing S.H.M. is v, they velocity of the particle at a distance equal to half of the amplitude [RPMT 2001]
A)
4v done
clear
B)
2v done
clear
C)
\[\frac{\sqrt{3}}{2}v\] done
clear
D)
\[\frac{\sqrt{3}}{4}v\] done
clear
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question_answer27)
The instantaneous displacement of a simple pendulum oscillator is given by \[x=A\cos \left( \omega t+\frac{\pi }{4} \right)\]. Its speed will be maximum at time [CPMT 2000]
A)
\[\frac{\pi }{4\omega }\] done
clear
B)
\[\frac{\pi }{2\omega }\] done
clear
C)
\[\frac{\pi }{\omega }\] done
clear
D)
\[\frac{2\pi }{\omega }\] done
clear
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