Defining Simple Harmonic Motion (SHM) Practice

Sample questions

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1. Sample 1difficulty 2/5

   For a simple pendulum (small angles), the period

   • A

     Is independent of amplitude

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   • B

     Decreases with amplitude

   • C

     Increases with amplitude

   • D

     Cannot be defined

   Why

   For small-amplitude pendulums, period is independent of amplitude. (For large angles, period increases slightly.)

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2. Sample 2difficulty 2/5

   For an object to undergo SHM, the restoring force must be

   • A

     Independent of position

   • B

     Constant

   • C

     Proportional to displacement

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   • D

     Proportional to velocity

   Why

   SHM requires $F = -k x$ — restoring and linear in displacement.

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3. Sample 3difficulty 4/5

   A particle of mass $m$ moves in a potential $U(x) = \tfrac{1}{2}\beta x^2$ with $\beta > 0$. What is the angular frequency of small oscillations?

   • A

     $\omega = \beta/m$

   • B

     $\omega = \sqrt{\beta/m}$

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   • C

     $\omega = \sqrt{m/\beta}$

   • D

     $\omega = \sqrt{2\beta/m}$

   Why

   Restoring force $F = -dU/dx = -\beta x$, giving $m\ddot x = -\beta x$, so $\omega = \sqrt{\beta/m}$.

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