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A mass m that has net electric charge Q is oscillating along the x-direction on one end of a spring (whose other end is anchored) of relaxed length s0. Suppose that someone then swirches on an electric field E that is uniform in space, constant in time, and which points in the +x direction. The entire system is then immersed in this electric field.

a. Set up the governing differential equation of motion for the mass in a coordinate system

with origin at the “anchored” end of the spring. Ignore gravity.

b. Without actually deriving it, what do you anticipate that the governing differential

equation in a “smart” coordinate system would be?

c. Go through steps analogous to those we went through in our text discussion to show that

the equivalent differential equation expressed in terms of the “right” variable is

independent ofE

Hint: As part of this, you will need to find the equilibrium position with the field “on.”

Any idea of where to start would be greatly appreciated, thanks!

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# Homework Help: Charged Particle Oscillating in External Constant Electric Field

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