time period by energy mathod questions with solutions

Showing 1–4 of 4 questions

• A/RmediumSimple Harmonic Motiontime period by energy mathod

  Choose the correct option for the following Assertion (A) and Reason (R).

  Assertion

  The effective inertial contribution of a uniform spring of mass mₛ, fixed at one end and oscillating longitudinally in the standard fundamental approximation, is mₛ/3.

  Reason

  The speed of spring elements varies approximately linearly from zero at the fixed end to the speed of the free end.

  Options

  • Option A

    Both A and R are true and R is the correct explanation of A.

  • Option B

    Both A and R are true but R is NOT the correct explanation of A.

  • Option C

    A is true but R is false.

  • Option D

    A is false but R is true.

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• MCQmediumSimple Harmonic Motiontime period by energy mathod

  A block of mass M is attached to the free end of a uniform spring of mass mₛ and spring constant k. The other end of the spring is fixed. During the fundamental longitudinal oscillation, the speed of the spring material varies approximately linearly from zero at the fixed end to the block speed at the free end. What is the approximate time period?

  Options

  • Option A

    2π√(M/k)

  • Option B

    2π√[(M+mₛ)/k]

  • Option C

    2π√[(M+mₛ/3)/k]

  • Option D

    2π√[(M+mₛ/2)/k]

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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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• NumericmediumSimple Harmonic Motiontime period by energy mathod

  A uniform spring of mass 3 kg and force constant 120 N/m is fixed at one end, and a block of mass 2 kg is attached to the other end. Using the standard effective spring mass mₛ/3 for the fundamental longitudinal oscillation, if ω² = N s⁻², find N.

  Your answer

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