(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the equation of motion for a particle of massmsubject 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)=Ce^{iwt}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)=Ce^{iwt}

3. The attempt at a solution

I took the derivative of the last equation listed in b twice to get x'(t)=iwCe^{iwt}and then x''(t)=i^{2}w^{2}Ce^{iwt}, which simplifies to x''(t)=-w^{2}Ce^{iwt}.

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.

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# Homework Help: Equation of motion solutions

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