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question_answer1) A particle is oscillating according to the equation\[X=7\cos 0.5\pi t\], where't' is in second. The point moves from the position of equilibrium to maximum displacement in time (in sec)?
question_answer2) The motion of a particle executing S.H.M. is given by\[x=0.01\text{ }sin\,\,100\pi \,\,(t+.05)\], where x is in meters and time is in seconds. The time period is (in sec)?
question_answer3) The displacement y of a particle executing periodic motion is given:\[y=4{{\cos }^{2}}\left( t/2 \right)\sin \left( 1000\,t \right)\]. This expression may be considered to be a result of the superposition of ... independent harmonic motions.
question_answer4) A particle is vibrating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and half kinetic? ( in cm)
question_answer5) The time - period of a particle undergoing S.H.M. is 16 sec. It starts its motion from the mean position. After 2 sec, its velocity 0.4 m/s. The amplitude is (in cm)?
question_answer6) A small body of mass 0.10kg is undergoing simple harmonic motion of amplitude 1.0 metre and period of 0.20 sec the maximum value of the force ( in N) acting on it?
question_answer7) Two pendulums have time-periods T and 5T/4. They starts S.H.M. at the same time form the mean position. What will be the phase difference between them after the bigger pendulum has completed one oscillation? ( in degree)
question_answer8) Two simple pendulums of lengths 1 meter and 16 meter respectively are both given small displacement in the same direction at the same instant. They will again be in phase after the shorter pendulum has completed n oscillations where n is-
question_answer9) A 2.0 kg particle undergoes SHM according to \[x=1.5\text{ }sin\left( \frac{\pi t}{4}+\frac{\pi }{6} \right)\](in SI units). What is the shortest time (in sec) required for the particle to move from \[x=0.75m\] to\[x=-0.75m\]?
question_answer10) Find the period of small oscillation of a simple pendulum of length \['\ell '\] if it's point of suspension O moves relative to the earth with a constant acceleration\[\bar{a}\], given \[\ell =30\text{ }cm\]and \[\left| {\bar{a}} \right|=g/2\]the angle between the vectors \[\bar{g}\]and \[\bar{a}\]is\[\beta =120{}^\circ \]. The period (in sec) of oscillation of the pendulum is
question_answer11) If natural frequency \[\omega \]of the system shown in figure is\[x\sqrt{\frac{k}{5m}}\], find x.
question_answer12) Initially the spring is in natural length, block A is at rest and block B is moving with speed 5 m/s towards right on frictionless surface as shown in figure. Find the maximum speed of block A during the motion in m/s.
question_answer13) Rod is massless and of length\[\ell \]. Find angular frequency \[\omega \](in\[{{s}^{-1}}\]) of small oscillation of the block of mass m, the hinge is frictionless. \[{{k}_{1}},{{k}_{2}},{{k}_{3}}\]are spring constants of the shown springs. Ignore gravity.\[\left( {{k}_{1}}={{k}_{2}}=10N/m,{{k}_{3}}=\frac{15}{4}N/m,\,\,m=250gm \right)\]
question_answer14) The potential energy of a particle of mass 1 kg in motion along the x-axis is given by\[U=(10-10\text{ }cos\text{ }6x)\text{ }J\]. If the period of small oscillations is \[\frac{1}{n}\] second, find the value of n. \[\left( {{\pi }^{2}}\approx 10 \right)\]
question_answer15) A spring of force constant \[k=300\text{ }N/m\]connects two blocks having masses 2 kg and 3 kg, lying on a smooth horizontal plane. If the spring block system is released from a stretched position, find the number of complete oscillations in 1 minute is 25 N, find the value of N. Take\[\pi =\sqrt{10}\].
question_answer16) A tiny mass performs S. H. M. along straight line with a time period of \[T=0.60\text{ }sec\]and amplitude A = 10.0 cm. Calculate the mean velocity (in m/sec) in the time to displace by \[\frac{A}{2}\]from mean position.
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