(a) Consider the system of Figure. The input signal x(t) = 3 is applied at t = 0. Find the...

(a) Consider the system of Figure. The input signal x(t) = 3 is applied at t = 0. Find the value of y(t) at a very long time after the input is applied.

(i)

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(ii)

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(b) Repeat Part (a) for the input signal x(t) = 3e4tu(t).

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(c) Repeat Part (a) for the input signal x(t) = 3 cos 4t. Use MATLAB to check your calculations.

(d) Repeat Part (a) for the input signal x(t) = 3ej4t.

(e) Repeat Part (a) for the input signal x(t) = 3 sin 4t. Use MATLAB to check your calculations.

(f) How are the responses of Parts (c) and (e) related?

(i) Find the time constants of the two systems in Part (a).

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(ii) In this problem, quantify the expression “a very long time.”