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PhoenixFire
 11 months 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 xcoordinate 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?
PhoenixFire
 11 months 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 xcoordinate 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?

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Mashy
 11 months ago
Best ResponseYou've already chosen the best response.2\[m \frac{d^2x}{dt^2} + eE_oSin(\omega t) = 0\] solve this differential equatinon :D

PhoenixFire
 11 months ago
Best ResponseYou've already chosen the best response.0@Mashy how did you come up with that differential?

PhoenixFire
 11 months ago
Best ResponseYou've already chosen the best response.0\(F=ma=eE(t)\) \(m\frac{d^2 x}{dt^2}=eE(t)\) Is this what you did?

Mashy
 11 months ago
Best ResponseYou've already chosen the best response.2yes yes.. sorry.. i was in a hurry and so i forgot to mention :D
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