Plot the response of a critically damped system (Eq. 2.80) for the following data using MATLAB:

a. \(x_{0}=10 \mathrm{~mm}, 50 \mathrm{~mm}, 100 \mathrm{~mm} ; \dot{x}_{0}=0, \omega_{n}=10 \mathrm{rad} / \mathrm{s}\).

b. \(x_{0}=0, \dot{x}_{0}=10 \mathrm{~mm} / \mathrm{s}, 50 \mathrm{~mm} / \mathrm{s}, 100 \mathrm{~mm} / \mathrm{s} ; \omega_{n}=10 \mathrm{rad} / \mathrm{s}\).

Equation 2.80:-

x(t) = [xo + (xo + wnxo)t]ewnt (2.80)