Chapter 16, Problem 12PS

(a)

To determine

Whether the differential equation $\frac{d^{2}y}{d{t}^2}+2\frac{dy}{dt}+26y=0$ represents an overdamped, critically damped, or under damped system.

(b)

To determine

The particular solution of the differential equation $\frac{d^{2}y}{d{t}^2}+2\frac{dy}{dt}+26y=0$ that satisfies the initial conditions $y(0)=1\text{and}{y}^{\prime }(0)=4$.

(c)

To determine

To graph: The particular solution $y=e^{-t}\cos 5t+e^{-t}\sin 5t$ using a graphing utility and explain how the graph illustrates the type of damping in part (a).