1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    [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

    User Avatar
    Science Advisor
    Homework Helper

    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...