Consider an electrical circuit comprising an inductor and a capacitor, with no external applied voltage, and no electrical resistance. The current, i, through the inductor is related to the charge, q, on the capacitor by the differential equation: where the inductance, L, and capacitance C, are positive constants.
(a)Given that the charge and the current are related through i=dq/dt derive a second order differential equation for q(t).
i know that the second order differential is
please help me solve the problem
b)assuming that the initial charge q(0)=q0 and the initial current i(0)=i0, show that
c) hence show that q(t) can be written as
where A and fi are to be determined
thanks for the help