I have a problem asking the following question:
We have a LRC circuit (L,R,C all in series) with a source \$ E(t) = Vsin(\omega t + \phi)\$. Is it possible to chose the phase \$\phi\$ so that we can cancel transient state and pass directly to steady state at \$ t = 0+ \$ ? The charge in the capacitor and the current in the inductor are initially zero.
Solutions book is vague and only states (translation might be bad):
Impossible due to quadrature relationships.
Could anyone tell me why it is impossible, in a detailed enough solution?
I did a similar exercise with a RC circuit, and came easily to the conclusion that, in order to cancel steady state, I must have \$ \phi = arctg \left ( RC \omega \right )\$. The way I solved it was to calculate for which phase I get zero in the Laplace transform of the response. The problem with a 2nd order system such as a LRC circuit is that I cannot use the same method rapidly and reliably enough because of how complicated the equations become when isolating the transient response in the s-domain.
Is there a way to know it's impossible without spending two hours in Laplace equations?