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Frequency and Period of SHM

AP Physics 1· difficulty 4/5

m k

A mass mm is hung from a vertical spring of stiffness kk and stretches it dd at equilibrium. The mass is then displaced and released. Compared to a horizontal spring with the same mm and kk, the vertical period is:

  • A

    Identical: T=2πm/kT = 2\pi\sqrt{m/k}

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  • B

    Longer due to gravity

  • C

    Shorter due to gravity

  • D

    Depends on amplitude

Explanation

Gravity simply shifts the equilibrium by d=mg/kd = mg/k. The restoring force about that new equilibrium is −kx-kx, so the period is unchanged: T=2πm/kT = 2\pi\sqrt{m/k}.

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