Chapter 3, Problem 3.41P

(a)

To determine

The general solutions $x\left(t\right)$ for underdamped, critically damped and overdamped motion.

(b)

To determine

Plot the results for $\frac{x\left(t\right)}{x_0}$ as a function of ${\omega }_{0}t$ in the three cases $\beta =\left(\frac{1}{2}\right){\omega }_0$, $\beta ={\omega }_0$ and $\beta =2{\omega }_0$.