## PhoenixFire one year ago 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?

1. Mashy

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

2. PhoenixFire

@Mashy how did you come up with that differential?

3. PhoenixFire

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

4. PsiSquared

Yes.

5. Mashy

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

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