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How to understand equations of simple harmonic motion

  1. Nov 9, 2004 #1
    hello...

    I was wondering if someone can help me fully understand the equations of SHM:

    x(t) = A cos (wt + theata)
    v(t) = -A sin (wt + theata)
    a(t) = -A cos (wt + theata)

    you see... i know that A is the amplitude and that theata is the phase shift. I know that w is agular frequency, but i dont know what it does and how to find period with it.

    My real problem is the t infron of w. I have no idea what that is and I have know idea how to use it in a calcuation.

    Can someone please explain to me a good general vieow of how to interpret these euqations.

    Thanks
     
  2. jcsd
  3. Nov 9, 2004 #2

    James R

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    The frequency of the oscillations is

    [tex]f = \omega / 2\pi[/tex]

    The period is:

    [tex]T = 1 / f = 2\pi / \omega[/tex]

    t is the time. For example, if you want to know where the object is at t=0, just plug in the t value:

    [tex]x(0) = A \cos(\omega \times 0 + \theta)[/tex]
    [tex]= A \cos(\theta)[/tex]
     
  4. Nov 9, 2004 #3
    t is just time, of course - plotted along the horizontal axis. [itex]\omega[/itex] is the angular speed in radians/sec. So [itex]\omega t [/itex] is just the angular displacement in radians. Since one complete cycle or circle is [itex]2\pi[/itex] radians, [itex]\omega t = 2\pi\nu t = 2\pi t/T[/itex]
     
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