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Find the displacement of the underdamped driven mass.

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data

    A mass "m" is oscillating on a spring in one direction. And the mass has a dampening constant ψ. The right end of the spring is attached to the mass, and the left end is driven by a force. For t<0, the spring end is at rest, but for t>0 the end oscillates with amplitude Acos(w(driving)*t). Find the displacement of the mass for t>0.

    2. Relevant equations

    x(0)=0
    v(0)=0
    x = Re[A(r) + iA(i)](cos(wt) + isin(wt))] ...... A(r) and A(i) are just variables

    3. The attempt at a solution

    Starting with x = Re[A(r) + iA(i)](cos(wt) + isin(wt))] we get x(real) = A(r)cos(wt) -A(i)sin(wt).

    Now ma = -kx - bv = Acos(w(driving)*t)
    and (β^2)*a + (β)*γ*v + ω^2 = Acos(w(driving)*t) .... where γ = ψ/m and ω^2 = k/m

    Now, I want to add the solutions for the homogeneous and non-homogeneous equations, and then satisfy all of my initial conditions. But, I'm not sure how to go about doing this.
     
  2. jcsd
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