Representing and Analyzing SHM

AP Physics 1· difficulty 2/5

0 T/2 T 3T/2 +v_max −v_max v

The graph shows v(t)v(t) for a mass-on-spring oscillator. At which instant is the mass at one of the <strong>amplitude positions</strong> (largest displacement)?

  • A

    t=3T/4t = 3T/4

  • B

    t=0t = 0

  • C

    t=T/2t = T/2

  • D

    t=T/4t = T/4

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Explanation

At the amplitude (turning points), velocity equals zero. On the graph the first zero after t=0t = 0 is at t=T/4t = T/4 (where vv is at a minimum of the cosine — actually vv starts from 00 going negative; zero at T/4T/4 corresponds to max negative displacement). Any zero-vv instant works; T/4T/4 is one such time.

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