The response of an initially relaxed linear circuit to a

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The response of an initially relaxed linear circuit to a signal V_s is e^{– 2t}u(t). If the signal is changed to (V_s + 2(dV_s/dt), then response will be

1. – 4e^{– 2t} u(t)
2. – 3e^{– 2t} u(t)
3. 4e^{– 2t} u(t)
4. 5e^{– 2t} 4(t)

Correct Option: B

When the excitation of alinear system is differential, the output also is the differentiation of previous output
∴ Response = e^{– 2t} u(t) + 2 d/dt[e^2t u(t)] = – 3e^{– 2t} u(t)