# Homework Help: Equation of motion solutions

1. Aug 28, 2008

### davesface

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. Aug 28, 2008

### HallsofIvy

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.

3. Aug 28, 2008

### davesface

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?