Circular Motion and SHM

"You are a ring bearer, Frodo. To bear a ring of power is to be alone"
Galadriel - The Lord of the Rings

In our discussion of SHM we have defined the angular frequency of the motion.

But why should an angular variable be part of the description of a linear oscillatory motion ?

Consider a particle of mass m undergoing uniform circular motion about the origin, with angular frequency and radius A. If the particle starts at the point (A,0), the projection on the x axis is given by

This equation describes SHM along the x axis, where A is the amplitude of the motion and the period is given by equation 2

. (Note that if the particle does not start on the x axis then a phase angle Ø is not zero.)
Similarly the projection of the motion on the y axis also describes SHM

Combining the x and y SHM motions we obtain the eqution of the circle

VLADIMIR: "That passed the time", ESTRAGON: "It would have passed in any case", VLADIMIR:"Yes, but not so rapidly"

Samuel Beckett - Waiting for Godot (1955)

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu