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At the time t=0, the charge on the condensator is 10μC and the current in the inductor is 0.3A. What is the current in the inductor as a function of time?

With:[itex]q = Q_mcos(\omega_0t+\phi)[/itex] we get that: [itex]I = Q_m\omega_0cos(\omega_0t+\phi + \pi/2)[/itex] (because I = dq/dt), where [itex]\omega_0 = 1/(√LC)[/itex]

I thought that the initial conditions would mean that I have to solve:

[itex]q(0) = 10*10^{-6} =Q_mcos(\phi) [/itex] and [itex]I(0) = 0.3 = Q_m\omega_0cos(\phi + \pi/2)[/itex]. But these equations have no solution(!)