Find the differential equation representing this system if

Question

Assignment

1. The output of a system with tido initial conditions is given in the Laplace frequency domain by the equation

Y(s) = (3s + 4) / (s³ + 2s² + 4s)

(a) Find the differential equation representing this system if the input is given x(t) = u (t)

(b) Design a circuit that implements this differential equation.

Hint: You can do if mire a resistor, a capacitor and an inductor.

(c) Find equations for the transient and steady state responses of the system. Use MATLAB to perform partial fraction expansion.

(d) Use MATLAB to plot the transient and steady sta. response of the system to an input x(t) = 10000 cos (120πt) u (t) given the initial conditions {dy (0^-) / dt} = 1.and y (0^-) = 1

2. The output of a system with zero initial conditions is given in the Laplace frequency domain by the equation

Y(s) = (s - 1) / s² [(s + 1)² + 9)

(a) Find the differential equation representing this system if the input is given by x (t) = u (t)

(b) Find equations for the zero-input (ZIR) and zero state (ZSR) responses of this system.

(c) Use MATLAB to calculate and create pole-zero plots for the ZIR and ZSR. Assume d²y (0^-) / dt² = 1, dy (0^-) / dt = -1, y (0^-) = -1, and x (0^-) = 0.

(d) Use MATLAB to plot the time domain ZIR, ZSR and tonal response using the initial conditions given in part c.