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Energy of Simple Harmonic Oscillators

AP Physics 1· difficulty 4/5

A 0.50 kg0.50\,\text{kg} block on a frictionless surface attached to a spring of stiffness 200 N/m200\,\text{N/m} has speed 4.0 m/s4.0\,\text{m/s} as it crosses equilibrium. What is the amplitude of its SHM?

  • A

    A=0.20 mA=0.20\,\text{m}

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  • B

    A=0.10 mA=0.10\,\text{m}

  • C

    A=0.40 mA=0.40\,\text{m}

  • D

    A=0.05 mA=0.05\,\text{m}

Explanation

Energy conservation: 12mv2=12kA2\tfrac{1}{2}mv^2=\tfrac{1}{2}kA^2, so A=vm/k=4.00.5/200=4.0(0.05)=0.20 mA=v\sqrt{m/k}=4.0\sqrt{0.5/200}=4.0(0.05)=0.20\,\text{m}.

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