Consider the system given by 0 1 (t) = |- where a > 0 and b...

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Consider the system given by 0 1 (t) = |- where a > 0 and b R. (a) Letb-0. Compute the damping ratio, and undamped and damped natural frequencies. (b) Let b = 0. Determine the type of the response for different values of a (i.e., free vibration, underdamped, overdamped, critically damped). -4 x(t) + [qu(t), -a y(t) = [10] x(t) + bu(t), (c) Assume the system is initially at rest, and let b = 0 and u(t) = 1, t 0. Use MATLAB to plot the response for all types determined in Part (b) (Use a typical value for a for each type). (d) Let b 0. How does it change your answers in Part (b)? Consider the system given by 0 1 (t) = |- where a > 0 and b R. (a) Letb-0. Compute the damping ratio, and undamped and damped natural frequencies. (b) Let b = 0. Determine the type of the response for different values of a (i.e., free vibration, underdamped, overdamped, critically damped). -4 x(t) + [qu(t), -a y(t) = [10] x(t) + bu(t), (c) Assume the system is initially at rest, and let b = 0 and u(t) = 1, t 0. Use MATLAB to plot the response for all types determined in Part (b) (Use a typical value for a for each type). (d) Let b 0. How does it change your answers in Part (b)?