Modeling with Periodic Functions

The equation d = 11 cos (8π/5 t) models the horizontal distance, d, in inches of the pendulum of a grandfather clock...

1.25 seconds

The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 15 cos (π/20 t). Howling does it take for the waterwheel to complete one turn?

10 seconds (wrong)

The depth of the water, d, at the end of a pier changes periodically as a function of time, t, in hours as shown in the graph below. According to the model, when will the next low tide occur? Let t = 0 be 12:00 a.m.

5:00 a.m. (Wrong)

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h= 3 sin (π/2 (t+2)) +5. Which of the following is the graph of this equation?

D

Suppose that you want to model the height of a rider on a Ferris wheel as a function nation of time, t, in minutes. If the rider is at the bottom of the Ferris wheel at t = 0 minutes, which of the following would be easiest to use?

The Cosine function reflected about its midline.

Which of the following situations can be modeled with a periodic function?

The height of a pebble stuck in the tread of a tire.

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin (bt) + k, for the height...

Y = 10 sin (π/15 t) + 30

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = asin (b (t-h) ) + k. What is the height of the ball at its equilibrium?

a feet (wrong)

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = -2 sin (π (t + 1/2) ) +5. Which of the following equations can also model this situation?

h = -2 cos (πt) + 5

The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 8 cos (π/10 t). What is the period of the function?

π/10 seconds (wrong)