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Amplitude of equation of motion

  1. Jun 13, 2012 #1
    Hello,

    I have worked out some force diagrams for forced oscillations and ended up with the solution as :

    mx_double_dot+rx_dot+kx=Pcos(Ωt)

    I am now asked to work out the amplitude. I know all of the variables except frequency(Ω). What equations can I use to find that?

    Thanks.
     
  2. jcsd
  3. Jun 13, 2012 #2

    Simon Bridge

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    [tex]m\ddot{x}+r\dot{x}+kx=P\cos(\omega t)[/tex]
    ... to see how the amplitude behaves, you'll need to solve the equation.
    The driving frequency is something you'd normally be given.

    I don't see a damping term - what do you think is likely to happen to the amplitude of the oscillations?
     
  4. Jun 13, 2012 #3
    I have worked out that this is a strongly dampered equation, so I expect the amplitude to die down quickly.

    So, without frequency, this cannot be done? The question I have is to get the amplitude in order to solve the frequency between certain amplitudes. That last part can be done on the computer.
     
  5. Jun 13, 2012 #4

    Simon Bridge

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    Oh I misread it - OK. So you have determined the system is overdamped which simplifies things - you need to find the natural frequency and damping ratio.

    You don't need the driving frequency to find the amplitude envelope - it's a decaying exponential: compare your equation with the general solutions.
    http://en.wikipedia.org/wiki/Harmonic_oscillator#Driven_harmonic_oscillators
     
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