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Equation of motion solutions

  1. Aug 28, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the equation of motion for a particle of mass m subject to a force F(x)=-kx where k is a positive constant. Write down the equation of motion as x''(t)=F/m. Then show that x(t)=Ceiwt is a solution to the equation of motion for any C as long as w has one of 2 possible values (i is the imaginary unit, w is omega, t is time). What are those values?

    There's more to it, but I am totally lost as to how I can at least start from this information.

    2. Relevant equations
    x''(t)=F/m
    F(x)=-kx, where k is a positive constant
    x(t)=Ceiwt

    3. The attempt at a solution
    I took the derivative of the last equation listed in b twice to get x'(t)=iwCeiwt and then x''(t)=i2w2Ceiwt, which simplifies to x''(t)=-w2Ceiwt.

    I guess that I really would just like to know if I'm anywhere in the ballpark for how the problem should begin. It's not a graded problem, but I hate leaving it unsolved.
     
  2. jcsd
  3. Aug 28, 2008 #2

    HallsofIvy

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    Looks to me like you are doing the problem backwards! You are first asked to write down the equation of motion. You give as "relevant equations" x"= F/m and F= -kx. Okay, looks to me like the equation of motion is x"= -kx/m.

    NOW you can argue that if x= Ceiwt, then x'= Ciweiw and x"= -Cw2eiwt= -w2(Ceiwt which is the same as -kx/m as long as w2= -k/m. That last equation should tell you what values w can have.
     
  4. Aug 28, 2008 #3
    2 questions there:
    1. Why is Ceiwt which is the same as -kx/m as long as w2= -k/m?
    2. How does w2= -k/m lead me to the values of w?
     
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