1. A mechanical control system can be described with following differential equation:
\ddot{y} + 3\dot{y} + 2y - u(t)
where $y(0) = -1$, $\dot{y}(0) = 2$ and $u(t)$ is a unit step.
a. Use analytical method (not Matlab) to find $y(t)$. That is, first perform Laplace
transformation on the equation, then solve for $Y(s)$. After that, use inverse Laplace
transformation to find out $y(t)$.
b. Use Matlab to plot the analytic solution of $y(t)$ you obtained in (a). Please show
your Matlab codes and the Matlab plot clearly.
c. Use Matlab step function to plot the step response of the system. Compare your
plot with the result in (b). Explain the differences and similarities between the results in
(b) and (c).
