Sinusoid Question

Question

A ball is attached to a string and swung in a vertical circle. The string is 28 inches and it completes one revolution in 3 seconds. If the closest the ball gets to the ground is 2 inches, find a sinusoid that models the height, h(t), of the ball t seconds after you start swinging. I can't figure out the amplitude or the vertical shift. I know that there is no horizontal shift. I figured out the period.

Answer 1

Amplitude = 28 (the length of the string)

 

Vertical Shift = height of midline above the ground = 2 + 28 = 30

 

Horizontal Shift depends on where the ball is when you start.  The zero position would be with the ball and string horizontal along the midline swinging up.  If you start with the ball hanging straight down, you are starting at the low point of the sinusoidal curve, so horizontal shift would be -pi/2.

 

y = 28 sin((2pi/3)t - pi/2) + 30