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Linear Algebra: Solving a system of equations for damped oscillation

  1. Apr 10, 2013 #1
    So we are given two equations:

    $$ \ddot{x} - \dot{x} - x = cost (t) $$

    and

    $$ x(t) = a sin(t) + b cos(t) $$

    The question asks to find a and b.

    How would one go about doing this? I thought maybe substituting the $$ cos(t) $$ from equation 1 into equation 2 would work but then what system of equations would I have to solve? I am completely clueless on how to set up this problem. Any suggestions and hints are appreciated.
     
  2. jcsd
  3. Apr 10, 2013 #2
    Was there any additional information?

    Try taking the first and second derivatives of x
     
  4. Apr 10, 2013 #3
    There was not much additional information which would have helped me arrive at a solution. What would I do after taking the second derivative of x with respect to t? Plug it into equation 1? But then How would I solve my equations then?
     
  5. Apr 10, 2013 #4
    Ok, just wondering.

    Take the first and second derivatives of x, then plug those into the first equation. You should see from there
     
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