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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
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