Question

An object is undergoing uniform circular motion. True or False: A graph of its position oscillates back and forth, but not with simple harmonic motion.

A.) True

B.) False

Answer 1

False. Because the motion undergoes Simple Harmonic Motion (SHM)

A point P moving on a circular path with a constant angular velocity is undergoing uniform circular motion. Its projection on the x-axis undergoes simple harmonic motion. Also shown is the velocity of this point around the circle, , and its projection, which is . Note that these velocities form a similar triangle to the displacement triangle.

To see that the projection undergoes simple harmonic motion, note that its position is given by where , is the constant angular velocity, and is the radius of the circular path. Thus,

The angular velocity is in radians per unit time; in this case radians is the time for one revolution . That is, . Substituting this expression for , we see that the position is given by:

The position of the projection of uniform circular motion performs simple harmonic motion, as this wavelike graph of versus indicates.