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Driving force in simple harmonic oscillator with exponential

  1. Sep 28, 2015 #1
    1. The problem statement, all variables and given/known data
    A particle in SHM is subject to a driving force F(t)= ma*e^(-jt). Initial position and speed equal 0. Find x(t).

    2. Relevant equations
    F = -kxdx = mvdv
    F(t) = F(0)*e^(iωt)
    x(t) = Acos (ωt +φ)

    3. The attempt at a solution
    I have no idea how to deal with the exponential term. I know I can put the t in e^(-jt) in terms of v, but that makes integration awfully messy. Any tips? Thanks!
     
  2. jcsd
  3. Sep 28, 2015 #2
    There are two forces here: the elastic force and the driving force. When you write Newton's second law you need to include both.
    -Kx+F(t)=ma

    This will result in a non-homogeneous second order differential equation.
    A possible solution will be an oscillation with the same frequency as the driving force's frequency.
     
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