Question

Prove mathematically that if a sinusoidal input is applied to a linear stable system then the...

Prove mathematically that if a sinusoidal input is applied to a linear stable system then the steady-state response is a scaled and phase-shifted version of the input.

Hints:

1. Assume a generic stable closed-loop transfer function.

2. Assume a generic sinusoidal input signal i.e. say ?(?) = ? sin(??)

3. Find c(t) and show mathematically that statement in the problem is satisfied.

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