# Speed of oscillation of free electrons

## Homework Statement

Find maximum speed of oscillation of a free electron near Earth’s surface due to
Sun’s electromagnetic field. Find out the ratio of maximum magnetic force acting
on the electron Fm to the maximum electric force Fe. Regard Sun’s radiation as
monochromatic with wavelength of 550 nm. Average intensity of Sun’s radiation
at Earth atmosphere is 1400 W/m2.

## Homework Equations

mx'' + m $$\Gamma$$ x' + m $$\omega$$02 x = eE

## The Attempt at a Solution

clearly the above equation is just a second order DE with a driving and damping force. My question is do I solve for omega? which would be $$\sqrt{ke/m}$$ ? Or is there another equation that I am possibly unaware of that could be of use?