Can anyone explain how the system of an electron placed outside of a ring of charge undergoes simple harmonic motion? I am asked to setup a SHM differential equation for a system that looks like this: http://people.rit.edu/agysps/courses/313_071web/class_wksheets/INTring_low.gif where P is an electron.

Question

Can anyone explain how the system of an electron placed outside of a ring of charge undergoes simple harmonic motion?  I am asked to setup a SHM differential equation for a system that looks like this: http://people.rit.edu/agysps/courses/313_071web/class_wksheets/INTring_low.gif where P is an electron.

anonymous · Answer

if an electron is placed along the axis of a positively charged ring, u can see the equation of the force acting on it is directly proportional to x, the distance from the ring, after neglecting certain values.

anonymous · Answer

F= -kpq(x)/$$(R^{2} + x^{2})^{3/2}$$

anonymous · Answer

if R>>x we get 
F= $$-kpq (x) / R^3$$

anonymous · Answer

a = -kpx/mr^3

anonymous · Answer

$$d ^{2}x/dt^{2}$$ = -(kpq / R^3)(x)

anonymous · Answer

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