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Frequency and Period of SHM

AP Physics 1· difficulty 4/5

m k k

A block of mass mm is held between two identical horizontal springs of stiffness kk (one on each side). What is the period of small oscillations?

  • A

    T=2π2m/kT = 2\pi\sqrt{2m/k}

  • B

    T=2πm/kT = 2\pi\sqrt{m/k}

  • C

    T=2πm/(2k)T = 2\pi\sqrt{m/(2k)}

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  • D

    T=πm/kT = \pi\sqrt{m/k}

Explanation

Both springs push back when displaced, so the effective stiffness is keff=2kk_{eff} = 2k. Hence T=2πm/(2k)T = 2\pi\sqrt{m/(2k)}.

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