Let Y(s) = L[y(t)] be the Laplace transform of the solution of a second-order differential equation representing a system with input x(t) and some initial conditions,

(a) Find the zero-state response (response due to the input only with zero initial conditions) for x(t) = u(t).

(b) Find the zero-input response (response due to the initial conditions and zero input).

(c) Find the complete response when x(t) = u(t).

(d) Find the transient and the steady-state response when x(t) = u(t).

(e) Use MATLAB to verify the above responses.

Transcribed Image Text:

X(s) s+1 Y (s) = .2 s + 2s + 1 s? + 2s +1