Chapter 16, Problem 13PS

(a)

To determine

Whether the differential equation $\frac{d^{2}y}{d{t}^2}+20\frac{dy}{dt}+64y=0$ represents an overdamped, critically damped, or under damped system.

(b)

To determine

The particular solution of the differential equation $\frac{d^{2}y}{d{t}^2}+20\frac{dy}{dt}+64y=0$ that satisfies the initial conditions $y(0)=2\text{and}{y}^{\prime }(0)=-20$.

(c)

To determine

To graph: The particular solution $y=e^{-4t}+e^{-16t}$ using a graphing utility and explain how the graph illustrates the type of damping in part (a).