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Representing and Analyzing SHM

AP Physics 1· difficulty 2/5

A mass m=0.25 kgm = 0.25~\text{kg} on a spring (k=100 N/mk = 100~\text{N/m}) oscillates with amplitude A=0.10 mA = 0.10~\text{m}. What is its maximum speed?

  • A

    0.40 m/s0.40~\text{m/s}

  • B

    1.0 m/s1.0~\text{m/s}

  • C

    4.0 m/s4.0~\text{m/s}

  • D

    2.0 m/s2.0~\text{m/s}

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Explanation

Energy: 12kA2=12mvmax⁡2\tfrac{1}{2}k A^2 = \tfrac{1}{2}m v_{\max}^2 ⇒vmax⁡=Ak/m=0.10100/0.25=0.10(20)=2.0 m/s\Rightarrow v_{\max} = A\sqrt{k/m} = 0.10\sqrt{100/0.25} = 0.10(20) = 2.0~\text{m/s}.

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