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I'm working on a series RLC problem where the input voltage is a sinusoidal function for all time. The catch is, for t < 0, the sinusoidal function is of greater magnitude than t >= 0. There is no phase or frequency change.

I am okay at working DC analysis for t < 0 and then AC, but I have no idea how to do this problem.

My guess is to do phasor/fourier analysis for t < 0, and once t = 0 I could use laplace domain now that there are "initial conditions" on the inductor and capacitor, then use those voltage drops to find my final equation for the voltage across the capacitor. I don't want anybody to do my homework for me, but pushing me in the right direction would be fantastic. Thank you.

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    \$\begingroup\$ Note that since this is a linear system, you can "split" the input signal into sinewave1, sinewave2 and a step (or pulse) function, determine the circuit's response to each of those and then simply add those up to get the response to the complete signal. \$\endgroup\$ – Bimpelrekkie May 6 '19 at 9:27
  • \$\begingroup\$ By inserting the energy of an impulse, occurring at T=0, you can make the stored energy have abrupt/step changes. \$\endgroup\$ – analogsystemsrf May 6 '19 at 9:31
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Since the signal is defined for all time, the circuit is in steady state for t < 0. You could simply calculate the steady state any way you know how. Then you could calculate the state of the system at t = 0 and continue with Laplace, as you suggested yourself.

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