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Hooke's Law: How to find Amplitude

  1. Jan 26, 2013 #1
    Hello all,
    (Newbie here so I hope I'm posting this in the right section, if not please guide me to the correct one)

    I'm studying Hooke's Law in Physics and there is something I can't understand.
    The equation for the Simple Harmonic Motion of a spring is given by [itex]x'' + wx =0[/itex]

    the general solution for the Differential equation above is given by: [itex]A sin (wt) + B cos (wt)[/itex]

    I came across a reference book that says: the amplitude is given by:
    [itex]sqrt {A^2 + B^2}[/itex]

    I'd like to understand how they got this?? Right now I know that w is the angular frequency and wt gives the phase angle, but A and B as constants make no sense to me, what are they and what do they mean physically?

    Any kind of answer would be greatly appreciated, please help me understand!!
    Thanks in advance!
     
    Last edited: Jan 26, 2013
  2. jcsd
  3. Jan 26, 2013 #2

    Doc Al

    User Avatar

    Staff: Mentor

    A more recognizable form of the general solution would be this:
    [tex]A\cos (\omega t + \phi)[/tex]
    Where A is the amplitude. Expand this (using a trig identity) and compare with the form you were given.
     
  4. Jan 26, 2013 #3
    Thanks a lot, I got it now :D
     
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