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Defining Simple Harmonic Motion (SHM)

AP Physics 1· difficulty 4/5

A particle of mass mm moves in a potential U(x)=12βx2U(x) = \tfrac{1}{2}\beta x^2 with β>0\beta > 0. What is the angular frequency of small oscillations?

  • A

    ω=β/m\omega = \beta/m

  • B

    ω=β/m\omega = \sqrt{\beta/m}

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  • C

    ω=m/β\omega = \sqrt{m/\beta}

  • D

    ω=2β/m\omega = \sqrt{2\beta/m}

Explanation

Restoring force F=−dU/dx=−βxF = -dU/dx = -\beta x, giving mx¨=−βxm\ddot x = -\beta x, so ω=β/m\omega = \sqrt{\beta/m}.

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