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Energy of Simple Harmonic Oscillators

AP Physics 1· difficulty 4/5

A mass on a spring oscillates with amplitude AA. At what displacement xx from equilibrium are the kinetic and potential energies equal?

  • A

    x=A/2x = A/\sqrt{2}

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  • B

    x=A/2x = A/2

  • C

    x=A/4x = A/4

  • D

    x=Ax = A

Explanation

Total energy is 12kA2\tfrac{1}{2}kA^2. Equal split means U=12kx2=14kA2U = \tfrac{1}{2}kx^2 = \tfrac{1}{4}kA^2, giving x=A/2x = A/\sqrt{2}.

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