In the above diagram,

i_in(t) = -0.5u(-t) + 2u(t) A
R = 2 Ω
L = 1 H
C = 8 mF

Find the zero-input, zero-state, and complete responses of v_C(t) and i_L(t) for t > 0.

This is what I have so far, and I think it's correct, but I am totally confused as to what I need to do to get the zero-input response. I'm not really sure if I understand it conceptually. I know it (obviously) involves turning off all input sources, but can I do it for any time value?

 

I'm not sure what your author means by "zero-input" or "zero-state". Could you look up those terms in your text and post a description? It's probably just a matter of a somewhat different terminology than I saw 25 years ago.

 

I'm not sure what your author means by "zero-input" or "zero-state". Could you look up those terms in your text and post a description? It's probably just a matter of a somewhat different terminology than I saw 25 years ago.

Yes - the same applies to me. I feel helpless with these terms.

 

The zero-input response of the circuit is the response to the initial conditions when all inputs are set to zero. The zero-state response is "the response to a specified input signal or set of input signals given that the initial conditions are all set to zero."

By linearity, the sum of the zero-input response and the zero-state response should provide an equation for the complete response of the circuit.