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Energy of Simple Harmonic Oscillators

AP Physics 1· difficulty 3/5

A spring oscillator passes through equilibrium at t=0t = 0. At what time is U first equal to K?

  • A

    T/4T/4

  • B

    T/6T/6

  • C

    T/2T/2

  • D

    T/8T/8

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Explanation

K=UK = U when ∣x∣=A/2|x| = A/\sqrt 2. From x=Asin⁡(ωt)x = A\sin(\omega t): sin⁡(ωt)=1/2⇒ωt=π/4⇒t=T/8\sin(\omega t) = 1/\sqrt 2 \Rightarrow \omega t = \pi/4 \Rightarrow t = T/8.

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