Chapter 8.5, Problem 39P

(a) Find numerical values of the constants and computer plot together on the same axes graphs of (5.30), (5.31) and (5.32) in order to compare overdamped, critically damped, and oscillatory motion. Suggested numbers: Let $\omega =1$, and $b=13/5,1,5/13$ for the three kinds of motion. Let $y(0)=1$ and $y^{\prime }(0)=0$.

(b) Repeat the problem with the same set of $\omega$ and $b$ values and with $y(0)=1$ but with $y^{\prime }(0)=1$.

(c) Again repeat, with $y^{\prime }(0)=-1$.