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Is there any specific impulse response (like there is one for a RC circuit) for a series RLC circuit and a LC circuit with the voltage taken across the capacitor or do we just say that the impulse responses for the 3 cases (under damped, critically damped and over damped) are too complex to be written though they do exist?

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  • \$\begingroup\$ It does exist, and my university wanted me to derive it in 15 mins of exam \$\endgroup\$ – Deep Dec 7 '17 at 7:17
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Yes, the impulse response exists for a series RLC circuit but you have to be aware that it is more complex than a simple RC or RL because the L and C form a resonant circuit and this gives rise (in notable cases) to a decaying sinewave response: -

enter image description here

The inductor and capacitor are equivalent to a spring and mass like below and virtually the same formulas apply: -

enter image description here

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  • \$\begingroup\$ Hmm just got four down votes on 4 different answers - something is going on. \$\endgroup\$ – Andy aka Jul 19 '17 at 18:25
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Andy is correct on how the rlc circuit behaves. I'm attaching a mathematical approach to the same below.enter image description here

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