Let's say an inductor is connected in parallel to a resistor and in parallel to a capacitor. At time t=0 the circuit is connected to a DC current source.The initial stored energy is zero. I have the solution in the text book under the section "The Step Response of a Parallel Circuit".
The current through the inductor is equal to the current of the current source plus a negative exponential multiplied to a sinusoidal function.
I understand that an inductor acts as a short for DC. But for the transient response the current through it will be zero and the current goes through the capacitor and resistor.
My question is where does the sinusoidal term comes from? Are there any physics behind it, or we just get it from analyzing the circuit?
What I am looking for is an answer like this:
When the DC current source is connected to a parallel RLC circuit, the capacitor acts as an open circuit, the inductor acts as short so all the current goes thorough the inductor but this the steady state response. For the instance that we close the switch(transient response) .....???...I am not sure what happens. It seems that the inductor becomes an open circuit(not sure why)and the capacitor and resistor current is negative exponential times sinusoidal (I don't understand this part either)