Simple Harmonic Motion questions with solutions

Showing 1–10 of 124 questions

• MCQmediumSimple Harmonic Motiondisplacement ,velocity and acceleration ,phasor diagram

  Two particles P₁ and P₂ execute SHM along the same straight line about the same mean position. Their displacements are x₁ = A sinωt and x₂ = A cosωt. At t = 0 they are at different positions. What is the first positive time at which they meet?

  Options

  • Option A

    T/12

  • Option B

    T/8

  • Option C

    T/6

  • Option D

    T/4

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• Multi-correctmediumSimple Harmonic Motiontime period by energy mathod

  Which statements correctly describe the energy method for identifying small SHM about a stable equilibrium?

  Select all that apply

  • Option A

    If U(x) = U₀+½kx² near equilibrium, then ω = √(k/m).

  • Option B

    If U(x) = U₀+αx²+βx⁴, then sufficiently small oscillations about x = 0 have ω = √(2α/m).

  • Option C

    Only the quadratic term in the potential determines the leading small-oscillation frequency.

  • Option D

    The energy method can determine the period without first writing the force explicitly.

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• MCQeasySimple Harmonic Motiontime period of linear shm

  A mass m is suspended from a uniform spring and oscillates with frequency ν₁. The same spring is cut into two equal halves, and the same mass is suspended from one half. If the new frequency is ν₂, what is ν₂ /ν₁?

  Options

  • Option A

    1

  • Option B

    2

  • Option C

    √2

  • Option D

    √3

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• MCQeasySimple Harmonic Motiontime period of linear shm

  A block of mass m is placed on a smooth horizontal surface and connected between two ideal springs fixed to opposite walls. The left spring has force constant k and the right spring has force constant 2k. If the block is displaced slightly and released, what is its angular frequency?

  Options

  • Option A

    √(k/m)

  • Option B

    √(2k/m)

  • Option C

    √(3k/m)

  • Option D

    √[k/(3m)]

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• NumericmediumSimple Harmonic Motiontime period of linear shm

  A body of mass 2 kg floats vertically in water. Its cross-sectional area at the water surface remains approximately constant at 0.01 m² during small vertical oscillations. Take water density 1000 kg/m³ and g = 10 m/s². If ω² = N s⁻², find N.

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• IntegermediumSimple Harmonic Motionkinetic and potential energy in shm

  At an instant, an SHM oscillator has displacement y = A cos30°. The amplitude is 40 cm and kinetic energy is 200 J. If the spring constant is 1.0 × 10ˣ N m⁻¹, find x.

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• MCQmediumSimple Harmonic Motiontime period of linear shm

  A uniform solid sphere of mass M and radius R rolls without slipping. A horizontal spring of force constant k is attached to the material point that is uppermost in the equilibrium position. For sufficiently small oscillations, the spring extension may be taken as twice the displacement x of the centre. What is the angular frequency?

  Options

  • Option A

    √[5k/(7M)]

  • Option B

    √[10k/(7M)]

  • Option C

    √[20k/(7M)]

  • Option D

    2√(k/M)

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• NumericmediumSimple Harmonic Motiondisplacement ,velocity and acceleration ,phasor diagram

  Two particles execute SHM according to x₁ = A sinωt and x₂ = A sin(ωt+π/3). If the first positive time at which their velocities are exactly equal is 5T/N, find N.

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• MCQeasySimple Harmonic Motiondisplacement ,velocity and acceleration ,phasor diagram

  A particle executing SHM is at x = A/2 and is moving towards the positive extreme. If the time period is T, how much additional time is required for the particle to reach x = A?

  Options

  • Option A

    T/12

  • Option B

    T/8

  • Option C

    T/6

  • Option D

    T/4

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• MCQmediumSimple Harmonic Motiontime period of linear shm

  A uniform U-tube of constant cross-sectional area contains a liquid column of total length L measured from one free surface to the other through the tube. The liquid is displaced slightly and released. Neglect viscosity. What is the time period of the resulting small oscillation?

  Options

  • Option A

    2π√(L/g)

  • Option B

    2π√[L/(2g)]

  • Option C

    2π√(2L/g)

  • Option D

    π√[L/(2g)]

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