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Thread: SHM

  1. #1
    Junior Member HoldingOn's Avatar
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    SHM

    A particle moves in SHM with acceleration given by x^(..)=-6x ms^2. When x=2, v=+-4.
    a. Find the period
    b. The amplitude
    c. Find the maximum velocity and acceleration

    Thanks in advance

  2. #2
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    Re: SHM

    From the reference sheet we have , where the period is given by

    .

    Clearly , so

    .

    Now,



    Substituting in the initial conditions gives .



    The maximum value of occurs when (). Therefore the maximum velocity is .

    Note that since must be non-negative, we have a restriction on , which is



    Therefore the amplitude is .

    Finally, going back to the first equation:



    The maximum acceleration occurs for the lowest possible value of , which is . This gives .
    HoldingOn likes this.

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