Frequency and Period of SHM Practice

Sample questions

5 of 31 — sign in to practice the rest with adaptive difficulty and mastery tracking.

1. Sample 1difficulty 1/5

   Doubling the length of a simple pendulum changes its period by a factor of

   • A

     $2$

   • B

     $\sqrt 2$

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   • C

     $4$

   • D

     $1/\sqrt 2$

   Why

   $T \propto \sqrt L$. Doubling $L$ → $\sqrt 2$ times $T$.

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2. Sample 2difficulty 1/5

   A spring-mass oscillator's amplitude is doubled. Its period

   • A

     Stays the same

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   • B

     Halves

   • C

     Doubles

   • D

     Quadruples

   Why

   $T = 2\pi\sqrt{m/k}$ — no $A$ dependence.

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3. Sample 3difficulty 1/5

   A spring-mass oscillator has period $T$. Doubling the mass changes the period by a factor of

   • A

     $\sqrt 2$

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   • B

     $1/\sqrt 2$

   • C

     $2$

   • D

     $1/2$

   Why

   $T \propto \sqrt m$. Doubling $m$ → $T \to \sqrt 2\, T$.

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4. Sample 4difficulty 1/5

   Quadrupling $k$ in a spring-mass oscillator (same $m$) changes the period by a factor of

   • A

     $2$

   • B

     $1/4$

   • C

     $4$

   • D

     $1/2$

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   Why

   $T = 2\pi\sqrt{m/k}$. $k \to 4k$ → $T \to T/2$.

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5. Sample 5difficulty 1/5

   A block of mass $0.50~\text{kg}$ oscillates on a spring with $k = 200~\text{N/m}$. What is the period of oscillation?

   • A

     $1.0~\text{s}$

   • B

     $0.31~\text{s}$

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   • C

     $0.10~\text{s}$

   • D

     $0.63~\text{s}$

   Why

   $T = 2\pi\sqrt{m/k} = 2\pi\sqrt{0.50/200} = 2\pi(0.05) \approx 0.314~\text{s}$.

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