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No need to calculate the moment of intertia of gears. It is small compare to the work loss from the other side. If you really need to calculate that. We know the gears sizes d=N/P (N:number of teeth ,P:diametial pitch, d:diateter) The same P is required to compose the gears. We known...

{M} [x] = [x']

Try Kirchhoff's circuit laws You have three loop. Besides, 8 Ohm:(4+2) Ohm

Slide crank is also a kind of four bar.(You need 4 vector to describe that,if it has offset.) The block count one. i=4 , j=4 .

v = vo + at s = 1/2 at2 v2 = v02+2as choose one

This is an exact equation. dy/dx = Numerator/Denominater D dx - N dy =0 \partialD/\partialy=\partialN/\partialx u (nearly)=D dx + N dy

Need numerical solve.

ac=gcos(theta)

Once the battery recharge,the current flow through the circuit and the LED lighted isn't it ?

Hi , How do you do ? you can try this answer. u=f(lnx -ln(1-x)-t) ln() for natural log. The method is here http://en.wikipedia.org/wiki/Method_of_characteristics" ----- ROC(Taiwan) is not PRC. http://en.wikipedia.org/wiki/Taiwan" -----