The input/output relationship of a LTIC with input x(t) and output y(t) is give by:
(D^3+7D^2+11D+5)y(t) = (D+3)x(t)
The input is sinewave x(t)=2sin(2t)u(t) and the initial conditions on the output and its first two derivatives at 0- are 1, 0, 0, respectively.
1) Find the transient and steady-state responses of the system using frequency domain methods.
2) Find the forced and natural responses of the system using frequency domain methods.
3)Find the 0+ conditions for the system's step response and impulse responses