Chapter 12, Problem 6P

(a)

To determine

To show: The position and velocity of the object for all time is $x_{\text{i}}\cos \omega t+\left(\frac{v_{\text{i}}}{\omega }\right)\sin \omega t$ and $-x_{\text{i}}\omega \sin \omega t+v_{\text{i}}\cos \omega t$ respectively.

(b)

To determine

To show: The $v^2-ax=v_{\text{i}}^2-a_{\text{i}}{x}_{\text{i}}={\omega }^2{A}^2$ by using $A$ to represent the amplitude of the motion.