The I/O relationship of a LTIC with input x(t) and output y(t) is given by: The

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The I/O relationship of a LTIC with input x(t) and output y(t) is given by: The input is given by x(t)=4cos(t)u(t), and the initial condition is y(0-) = 1, y(0-) = 0. Find the transfer function, poles, zeros and modes of the system. Find the zero input and zero state response of the system using Frequency domain methods. Find the transient and steady-state responses of the system using FD methods. Find the forced and natural responses of the system using FD methods. Find the initial conditions which will result in a zero transient response for the system. Plot the total response y(t) of the system using MATLAB . Draw the controllable canonical realization for this system Find the 0+ conditions for the system's step response .

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