Chapter 13, Problem 53P

An object undergoes simple harmonic motion in two mutually perpendicular directions, its position given by $\stackrel{\to }{r}=A\sin \omega t\hat{i}+A\cos \omega t\hat{j}$. (a) Show that the object remains a fixed distance from the origin (i.e., that its path is circular), and find that distance, (b) Find an expression for the object’s velocity, (c) Show that the speed remains constant, and find its value, (d) Find the angular speed of the object in its circular path.