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Spring Energy

  1. Feb 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Using x(t)= A cos(wt+phi) verify that the total energy is conserved.

    2. Relevant equations
    V(x)= Integral x to x1 F(x)dx

    3. The attempt at a solution

    I thought about using the aboved equation but have no idea where to start.
  2. jcsd
  3. Feb 20, 2010 #2
    F=ma so you can differentiate x[t] twice for a[t].Integrate F[t]=ma[t] w.r.t dx (you would have to make a substitution for x for that).You would also think K[t]=1/2m*v*v where v=v[t] at general instant t.
    Add and you will have a quantity independent of t.
  4. Feb 21, 2010 #3
    I am not sure how to make a substitution for dx.
  5. Feb 22, 2010 #4
    Well dx= vdt. Turns out a pretty lengthy problem after all. Will be happy to help further, if needed.
  6. Feb 22, 2010 #5
    Instead of your approach, I used F=-kx and integrate to get 1/2kx^2

    x(t) is given so I have an equation.
    w=sqrt (k/m)
    so things actaully worked nicely. and It was only a page of work.
  7. Feb 22, 2010 #6
    Well that is how you presented the problem. All textbooks use F=-kx to prove the result.
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