Jim S. answered • 07/06/14

Physics (and math) are fun, really

Allison,

There are 2 circuits, the one on the right is an RC circuit and the one in the left is an LCR circuit. If we start with the RC circuit and apply the loop theorem (conservation of energy) we get -iR-q/C=0 these are the voltage drops across the resistor and the capacitor traversing the circuit clockwise. Now remembering that i=dq/dt this relation give a differential equation for the charge on the capacitor R*dq/dt +q/C=0.

If you do the same for the RCL circuit we get iRR+Ldi/dt+q/C=0 where iRR is the voltage drop across the resistor, Ldi/dt across the inductor and q/C across the capacitor. Using i=dq/dt and di/dt= d

^{2}q/dt^{2}givesLd

^{2}q/dt^{2}+RRdq/dt + q/C=0 and the other equation is Rdq/dt+q/C=0 all in terms of the charge on the capacitor . Using these two fundamental equations and the definitions you should be able to derive the form listed in the reference document. Try it...Jim