1. The problem statement, all variables and given/known data The equation of motion of a free electron in an electric field is m((d^2)x)/(dt^2) = -eE (Eq. 1) If x and E have the time dependence exp(iwt), where w=angular frequency, then -(w^2)mx = -eE (Eq. 2) What does the time dependent function whose second derivative equals -(w^2)x look like? 3. The attempt at a solution I know from my papers that the electromagnetic wave is given by E=E0exp(iwt), and I guess the equation I'm after looks similar. The second derivative of x*exp(iwt) would give me the correct answer, but x=x0*exp(iwt) doesn't seem to do, because equation 2 says x and not x0.