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A piece of wire of mass m and resistance R forms a circular ring of area A. It is suspended by an insulatd, massless rod of lengthlto form a frictionless pendulum in the presence of a uniform, vertical magnetic field B. The normal to the ring is parallel to its velocity. Find the time required for the energy of a small oscillation of the pendulum to decay to 1/e of its original value.

What I have so far:

I have the differential equation for the damped harmonic oscillator:

[tex] m\ddot{x}+\frac{mg}{l} sin[\theta]+F_B = 0 [/tex]

where [tex] F_B [/tex] is the damping force. Basically I know that I want to find the torque, not the force at first then relate this back to the force in the end. I am having a really hard time finding [tex] T_B [/tex]. The problem I am having with the torque is finding the correct differential length to integrate so that my L x B term actually damps out the motion. Please help.

Thanks

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# Homework Help: Damped pendulum

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