Chapter D2.3, Problem 50E

a.

To determine

To find: The general solution of the given differential equation if $\omega \ne {\omega }_0$.

b.

To determine

To solve: The given initial value problem and show that $y=\frac{a}{{\omega }_0{}^2-{\omega }^2}\left(\cos \omega t-\cos {\omega }_{0}t\right)$.

c.

To determine

To describe: The graph of the above solution y, when $a=1,\omega =5\text{ and }{\omega }_0=6$.

d.

To determine

To rewrite: The solution of the given differential equation in terms of a product of two sine function.

e.

To determine

To interpret: The graph of part (c) and identify the two frequencies in the solution.