Question

A wooden horse on a merry-go-round moves 12 inches above and 12 inches below its center position. It takes the horse 10 seconds to make 1 complete up-and-down movement

a. Write an equation that gives the horse’s vertical position y at time t if the horse is at its center position when t=0.

Answer 1

The form of an equation is:
y = a sin ( b t ) , because it is at its center position when t = 0.
a = 12 ( amplitude );
T = 2π / b ( period )
10 = 2 π / b
b = 2 π / 10
b = π / 5
Answer:
y = 12 · sin ( π/5 · t )