Chapter 4.1, Problem 2E

If $F_{\text{ext}}\left(t\right)=0$, equation $\left(3\right)$ becomes

$m{y}^{″}+b{y}^{\prime }+ky=0$.

For this equation, verify the following:

a. If $y\left(t\right)$ is a solution, so is $cy\left(t\right)$, for any constant $c$.

b. If $y_1\left(t\right)$ and $y_2\left(t\right)$ are solutions, so is their sum $y_1\left(t\right)+y_2\left(t\right)$.