# deriving differential equation of a cart moved by a motor

This is homework and I'm having some trouble getting started. How do I go from whats given to the form that they ask for? Normally in something like this I would try to balance torque, but I'm not quite sure how to set it up in this case with voltage.

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A hint to get you started: $\dot x_c = R \dot \phi_d = \frac{R}{k}\dot \phi_m$ –  Alfred Centauri Oct 1 '12 at 19:31
@AlfredCentauri thanks! that was it, I subbed out phi-dot-m from eqn 1 and substituted i in terms of fc. –  mugetsu Oct 1 '12 at 21:33