Chapter 13.2, Problem 52E

To determine

To show: The expression $\text{r}″\left(t\right)+{\omega }^2\text{r}\left(t\right)$ is equals to 0 when the vector $\text{r}\left(t\right)=\text{a}\cos \omega t+\text{b}\sin \omega t$ where $\text{a}$ and $\text{b}$ are constant vectors.