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Masses and charges oscillating

by tunnelj
Tags: charges, masses, oscillating
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tunnelj
#1
Feb12-07, 09:30 PM
P: 1
1. The problem statement, all variables and given/known data

3 masses m, all with charge q, attached by two ropes of length d. the system is oscillating with small perturbations around a configuration where the three are in a straight line. Find q, given the period T, d, and m.

2. Relevant equations



3. The attempt at a solution
I'm taking the mode where the center mass moves up and down and the outer masses do the opposite. Take the origin as the location of the center mass when the three are in a line (along x axis).

Define y as the vert. displacement of the center mass. By cons. of p, the outer masses will be displaced y/2.

xleft=-dcos(theta) yleft = y/2 = (1/3)dcos(theta)
xcenter=0 ycenter = -y = -(2/3)dcos(theta)
xright=dcos(theta) yright = y/2 = (1/3)dcos(theta)

Tleft=(m/2)*([dsin(theta)thetadot]^2+[(1/3)dsin(theta)thetadot]^2)
Tcenter=(m/2)*[(2/3)dcos(theta)thetadot]^2
Tright=Tleft

V=2(kq^2)/d))+(kq^2)/(2dcos(theta))

I'm using the Lagrangian method, obviously. The issue that I'm having is that, after turning that crank, I still end up with a term that contains thetadot, which I don't really expect (physically). In fact, I expect it be be SHM (thetadoubledot = -(C^2)theta). The thetadot terms _almost_ cancel, but don't quite.

So... where have I gone off of the tracks?
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