Simple Harmonic Motion questions with solutions

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• NumericmediumSimple Harmonic Motion

  A simple harmonic motion is y = 5[sin(3πt) + √3 cos(3πt)]. What is the amplitude (in cm) if y is in m?

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• MCQmediumSimple Harmonic Motion

  A simple harmonic motion having an amplitude A and time period T is represented by the equation: y = 5 sin π(t + 4) m. Then the values of A (in m) and T (in s) are :

  Options

  • Option A

    A = 5; T = 2

  • Option B

    A = 10 ; T = 1

  • Option C

    A = 5 ; T = 1

  • Option D

    A = 10 ; T = 2

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• ParagraphmediumSimple Harmonic Motion

  A particle of mass m moves on a smooth horizontal line AB of length a. At a point P, a force mg(AP)/a acts towards A and another force 2mg(BP)/a acts towards B.

  Sub-question 1

  Find its time period when released from rest from mid-point of line AB.

  Options

  • Option A

    T = 2π√(3a/g)

  • Option B

    T = 2π√(a/2g)

  • Option C

    T = 2π√(a/g)

  • Option D

    T = 2π√(a/3g)

  Sub-question 2

  If the force acting towards A stops acting when the particle is nearest to B then find the velocity with which it crosses point B.

  Options

  • Option A

    √(2ga)/3

  • Option B

    √(2ga)/6

  • Option C

    √(2ga)/5

  • Option D

    √(ga)/3

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• NumericeasySimple Harmonic Motiondisplacement ,velocity and acceleration ,phasor diagram

  Two particles execute SHM on the same line according to x₁ = 4sinωt cm and x₂ = 4cosωt cm. If their maximum possible separation is N√2 cm, find N.

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• MCQmediumSimple Harmonic Motion

  At time t = t₀ a vertically oscillating spring-mass system is at its lowest point. At that instant gravity is switched off. Which graph correctly describes the subsequent displacement from the original equilibrium position?

  

  Options

  • Option A

    
  • Option B

    
  • Option C

    
  • Option D

    

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• MCQmediumSimple Harmonic Motion

  A particle moving along the x-axis has potential energy U(x) = k[1 - exp(-x²)], where k > 0. Which statement is correct?

  Options

  • Option A

    at point away from the origin, the particle is in unstable equilibrium.

  • Option B

    for any finite non-zero value of x, there is a force directed away from the origin.

  • Option C

    if its total mechanical energy is k/2, it has its minimum kinetic energy at the origin.

  • Option D

    for small displacements from x = 0, the motion is simple harmonic.

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• Multi-correctmediumSimple Harmonic Motion

  For a body executing SHM with amplitude A, time period T, maximum velocity vₘₐₓ and phase constant zero, which statements are correct?

  Select all that apply

  • Option A

    At y = A/2, v > vₘₐₓ/2

  • Option B

    v = vₘₐₓ/2 for |y| > A/2

  • Option C

    For t = T/8, y > A/2

  • Option D

    For y = A/2, t < T/8

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• MCQmediumSimple Harmonic Motionkinetic and potential energy in shm

  A particle executes SHM of amplitude A. At a certain instant its kinetic energy is three times its potential energy. What is the magnitude of its displacement from the mean position at that instant?

  Options

  • Option A

    A/4

  • Option B

    A/2

  • Option C

    A/√2

  • Option D

    √3A/2

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• MCQeasySimple Harmonic Motionkinetic and potential energy in shm

  A particle executes SHM. The ratio of potential energy to kinetic energy when its displacement is half the amplitude is:

  Options

  • Option A

    1 : 1

  • Option B

    2 : 1

  • Option C

    1 : 4

  • Option D

    1 : 3

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• MCQmediumSimple Harmonic Motionangular shm and its time period

  Statement I: A pendulum is taken from Earth to a planet having four times Earth's mass and twice Earth's radius; its time period remains the same. Statement II: The time period of a simple pendulum depends only on the gravity of the planet.

  Options

  • Option A

    Statement I is true but Statement II is false

  • Option B

    Statement II is true but Statement I is false

  • Option C

    Both statements are false

  • Option D

    Both statements are true

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