Vibrations and Waves · Problem 1-12

The superposition of periodic motions — A.P. French

Physics — Waves · simple-harmonic-motion-circular

Problem

A point moves in a circle at a constant speed of 50 cm/sec. The period of one complete journey around the circle is 6 sec. At

t = 0

the line to the point from the center of the circle makes an angle of

30°

with the

x

axis. (a) Obtain the equation of the

x

coordinate of the point as a function of time, in the form

x = A\cos(\omega t + \alpha)

, giving the numerical values of

A

\omega

, and

\alpha

. (b) Find the values of

x

dx/dt

, and

d^2x/dt^2

t = 2

sec.