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Show that ____ is a solution to the differential equation model?

  1. Oct 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Trying to go over this part of my test review. I'm not understanding how to do this. The specific problem which I actually have worked out in my notes:

    A diff equation model of the motion of a spring where x is displacement from the spring's natural length, k is the spring constant, and m is the mass as follows:

    (d^2*x)/(d*t^2) = k/m * x

    Show that x(t)=sin(sqrt(k/m)*t) + 2cos(sqrt(k/m)*t) is a solution to the model.

    3. The attempt at a solution

    My notes appear to take the first, then the second dir. of the second function there. But thats all I can make sense of. Maybe I'm not understanding how to take the dir of these functions I'm not sure.

    For example on the second to the last line, how am I supposed to simplify -k/m (sin(sqrt(k/m)t) + 2cos (sqrt(k/m)t)



    thanks for any help!
  2. jcsd
  3. Oct 5, 2009 #2


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    Because you just said that x=(sin(sqrt(k/m)t) + 2cos (sqrt(k/m)t) ?
  4. Oct 5, 2009 #3
    uhhh...thanks? Since somebody answered I won't get a real answer now. :(
  5. Oct 5, 2009 #4


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    Uhh... that was a real answer?
    Notice how you assume that x is sin(sqrt(k/m)*t) + 2cos(sqrt(k/m)*t) to start your answer.

    Notice how you want to replace the bolded portion with x. Notice how x is assumed to be exactly the bolded portion.
  6. Oct 5, 2009 #5
    Yes, I see what you're saying, sorry.

    I gave the second to the last line as an example of how I don't fully understand the process.

    To take the derivative or second derivative of the function do I sub something for sqrt(k/m)?

    sin(u*t) + 2cos(u)*t

    Like that?
  7. Oct 5, 2009 #6


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    You can but you should be able to use the chain rule without having to substitute like that. It is, after all, just a constant: the derivative of f(ax) is af '(ax).
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