Periodic Motion?

Question

A person rides on a Ferris wheel that rotates with constant angular speed. If the Sun is directly overhead, does the person's shadow on the ground undergo periodic motion? Does it undergo simple harmonic motion? Explain.

Please let me know if I'm on the right track, thanks!
A motion that repeats itself over and over is referred to as periodic motion. A particular type of periodic motion is simple harmonic motion. An example of this is the oscillation of a mass attached to a spring. Simple harmonic motion does not require mass. It so happens that a particular mass/force situation results in simple harmonic motion. However, if the movement of anything obeys x=A sin(Bt) then it is SHM. If a person rides on a Ferris wheel that rotates with constant angular speed and the Sun is directly overhead, the person’s shadow would undergo periodic motion. The shadow undergoes periodic motion, with the same period as the period of the Ferris wheel’s rotation.

Answer 1

The projection of the shadow of a person sitting on the ferris wheel that rotates at constant angular frequency will be described by simple harmonic motion.

The motion of a projection of an object undergoing uniform circular motion into one dimension is described by the equation X=A*sin (omega*t) where omega=angular freuency. You should diagram it and work it out to convince yourself. If you set theta=0 and X=0 when the person is at the 12 o'clock position on the ferris wheel, and work out the position of the shadow with the sun directly overhead, you'll find the position of the shadow to be exactly that equation. Just assume he sun is infinitely away compared to the diameter of the ferris wheel and you won't have to worry about changing incident angle of the sun's rays on the person as he travels around the ferris wheel.