Oscillations MCQs for NEET — Physics Questions with Answers

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A body is executing Simple Harmonic Motion. At a displacement x its potential energy is E1 and at a displacement y its potential energy is E2. The potential energy E at displacement x+y is 

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Explanation

(b)   E1=12Kx2x=2E1K, E2=12Ky2y=2E2K

      and E=12K x+y2x+y =2EK

      2E1K+2E2K=2EKE1+ E2=E

The equation of motion of a particle is d2ydt2+Ky=0 where K is positive constant. The time period of the motion is given by

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Explanation

(c)   On comparing with standard equation d2ydt2+ω2y=0 we get ω2=Kω2πT=KT=2πK

The kinetic energy of a particle executing S.H.M. is 16 J when it is in its mean position. If the amplitude of oscillations is 25 cm and the mass of the particle is 5.12 kg, the time period of its oscillation is -

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Explanation

a)          At mean position, the kinetic energy is maximum.

      Hence 12ma2ω2=16

On putting the values we get ω=10 T= 2πw=π5sec

A pendulum has time period T. If it is taken on to another planet having acceleration due to gravity half and mass 9 times that of the earth then its time period on the other planet will be

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Explanation

(d) T=2πlgT1gTpTe=gegp=21Tp=2T

A particle in SHM is described by the displacement equation xt=Acos ωt+θ. If the initial position of the particle is 1 cm and its initial velocity is πcm/s, what is its amplitude? (The angular frequency of the particle is π s-1)

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Explanation

(b) Given, v=πcm/sec, x=1 cm and ω=πs2 using v=ωa2-x2π=πa2-11=a2-1a=2cm. 

A simple pendulum hanging from the ceiling of a stationary lift has a time period T1. When the lift moves downward with constant velocity, the time period is T2, then

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Explanation

(d) T1g and g is same in both cases so time period remains same.

If the length of a pendulum is made 9 times and mass of the bob is made 4 times , then the value of time period becomes

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Explanation

(a) T=2πlgTl, hence if l made 9 times, T becomes 3 times.

Also time period of simple pendulum does not depends on the mass of the bob.

The period of a simple pendulum measured inside a stationary lift is found to be T. If the lift starts accelerating upwards with acceleration of g/3 then the time period of the pendulum is

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Explanation

(c) For stationary lift T1=2πlg 

For ascending lift with acceleration a,

T2=2πlg+aT1T2=g+agTT2=g+g3g=43T2=32T

 

The time period of a simple pendulum of length L as measured in an elevator descending with acceleration g3 is

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Explanation

(c) The effective acceleration in a lift descending with acceleration g3 is geff=g-g3=2g3so, T=2πLgeff=2πL2g/3=2π3L2g

 

If a body is released into a tunnel dug across the diameter of earth, it executes simple harmonic motion with time period

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Explanation

(a)

Acceleration due to gravity at a depth d below the surface of the earth;g'=g1-dR=gRR-d=gRxg'xω2=gRT=2πReg

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