Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Driven Harmonic Sys. Displacement Amp.

  1. Sep 9, 2011 #1
    1. The problem statement, all variables and given/known data
    I need to find the steady state displacement amplitude for a driven harmonic system.

    2. Relevant equations
    mass (m) = .5kg
    stiffness (s) = 100 N/m
    mechanical resistance (Rm) = 1.4 kg/s
    force (f) = 2cos5t

    3. The attempt at a solution
    What I know:
    angular freq (w) = 5 rad/sec
    magnitude of force (F) = 2N
    necessary diff. eq.: m[itex]\ddot{x}[/itex] + Rm[itex]\dot{x}[/itex] + sx = Fexp(iwt)
    complex displacement: x=[itex]\frac{1}{iw}[/itex][itex]\frac{Fexp(iwt)}{Rm + j(wm-s/w)}[/itex]

    I can ignore exp(iwt) because |exp(iwt)|=1.

    So I need to find the magnitude of the complex displacement (while ignoring exp(iwt)) but I just don't remember how to deal with complex numbers. I've basically got all the values for what's in the complex equation I just don't know what to do with it!
    Last edited: Sep 9, 2011
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?