# Repeat Problem 3-34 for the differential equation given in Problem 3-35. Problem 3-34 Consider…

Repeat Problem 3-34 for the differential equation given in Problem 3-35.

Problem 3-34

Consider the differential equation given in Problem 3-33. Use MATLAB to

(a) Find the partial-fraction expansion of Y(s) / R(s).

(b) Find the Laplace transform of the system.

(c) Find the output y(t) for t ≥ 0 when r(t) = us(t).

(d) Plot the step response of the system.

(e) Verify the final value that you obtained in Problem 3-33 part (f).

Problem 3-33

The differential equation of a linear system is

where y(t) is the output, and r(t) is the input.

(a) Write the state equation of the system. Define the state variables from right to left in ascending

order.

(b) Find the characteristic equation and its roots. Use MATLAB to find the roots.

(c) Find the transfer function Y(s) / R(s).

(d) Perform a partial-fraction expansion of Y(s) / R(s).

(e) Find the output y(t) for t ≥ 0 when r(t) = us(t).

(f) Find the final value of y(t) by using the final-value theorem.

Problem 3-35

Repeat Problem 3-33 for the following differential equation:

Problem 3-33

The differential equation of a linear system is

where y(t) is the output, and r(t) is the input.

(a) Write the state equation of the system. Define the state variables from right to left in ascending

order.

(b) Find the characteristic equation and its roots. Use MATLAB to find the roots.

(c) Find the transfer function Y(s) / R(s).

(d) Perform a partial-fraction expansion of Y(s) / R(s).

(e) Find the output y(t) for t ≥ 0 when r(t) = us(t).

(f) Find the final value of y(t) by using the final-value theorem.