A buoy oscillates in simple harmonic motion according to the motion of waves at sea. An observer notes that the buoy moves a total of 6 feet from its lowest point to its highest point. The buoy returns to its highest point every 15 seconds.

Question

Amplitude: 6 feet
Period: ???
Frequency: ???
Possible equation:???

Answer 1

Period = time per cycle = 15 seconds
frequency = 1 / period = 1/15 hz
amplitude= 3 ft because its actually the distance from the center to each side.

from there just put it into standard form.

Answer 2

Would I use cosine or sine?

Answer 3

It doesn't make a difference as long as your value for when t = 0 is correct since sin is just cosine phase shifted by pi/2.

Cosine is probably easier in this case because then you wont need to do a shift.

Answer 4

nevermind I thought it said that it began at its highest point.

Since they didn't specify any initial conditions you're free to use either sin or cosine with no phase shift.

Answer 5

How do I find omega (ω)?

Answer 6

w = 2*pi*period