The shadows of a merry go round (SHM)?

[donkeycopter]

The sun is setting and shines light in such a way that it is directly behind a merry go round, so its shadow is projected onto a wall behind it. The merry-go-round is one where the horses move up and down vertically as they move around the circle. The amplitude of this is 0.5m, and the period of their movement around the circle is 10s. The mass of each horse is 100kg. In relation to simple harmonic motion, and uniform circular motion, describe the shadows projected onto the wall. Calculate the centripetal acceleration and centripetal force of the horse in their motion.

Homework Equations

T=2pi sqrt(m/k)
v=rw
w=2pi/T
a=v^2/r

The Attempt at a Solution

Well as far as I can tell, this problem is describing the projection of simple harmonic motion onto a flat surface. The shadows should therefore show a sine wave with the amplitude 0.5m.

From there however, I don't even know where to start!

 

[jbsteele]

I know that centripetal acceleration and force are related to uniform circular motion but I'm not sure how this relates to the problem.Centripetal acceleration is given by a=v^2/r, where v is the velocity of the horse and r is the radius of the merry-go-round. The velocity can be found using w=2pi/T, where T is the period of the motion. Therefore, we have v=rw, so a=r^2w^2/r = rw^2.The centripetal force is given by F=ma, where m is the mass of the horse and a is the centripetal acceleration. Therefore, F=mrw^2.