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.