A free electron in an oscillating field experiences a force $\mathbf{F}=-e\mathbf {E}(t)$, where $\mathbf {E}(t)=\mathbf {E_0}sin(wt)$ and $\mathbf {E_0}=(E_0,0,0)$

Question

A free electron in an oscillating field experiences a force $\mathbf{F}=-e\mathbf {E}(t)$, where $\mathbf {E}(t)=\mathbf {E_0}sin(wt)$ and $\mathbf {E_0}=(E_0,0,0)$ <- completely in the x direction.

if x(t) is the x-coordinate of the electron and we assume $x(0)=\frac{dx}{dt}(0)=0$

How do we find the equation of motion along the 'x' axis from this information?

anonymous · Answer

$$m \frac{d^2x}{dt^2} + eE_oSin(\omega t) = 0$$
solve this differential equatinon :D

phoenixfire · Answer

@Mashy  how did you come up with that differential?

phoenixfire · Answer

$F=ma=-eE(t)$
$m\frac{d^2 x}{dt^2}=-eE(t)$

Is this what you did?

anonymous · Answer

Yes.

anonymous · Answer

yes yes.. sorry.. i was in a hurry and so i forgot to mention :D