Modeling with Periodic Functions Answers

The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation . What is the maximum displacement of the tuning fork?

A rider boards a Ferris wheel 10 feet above ground level. The diameter of the Ferris wheel is 50 feet and the wheel completes one full rotation every 24 seconds. Which graph represents the relationship between time and height off the ground?

A driver runs over a nail, puncturing the tire without causing a leak. The position of the nail in the tire, with relation to the ground, while the car is moving at a constant speed is shown in the table. Time (s)Approximate height of the nail off the ground (inches)000.012.10.027.60.0314.90.0421.50.0525.50.0625.50.0721.5Which key feature of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire?

The equation can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate.

The height, d, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . The ball is released from its lowest point at seconds. Using your knowledge of the general form of sine and cosine functions, which of the following equations can also model this situation?

The height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be modeled by the equation . What is the minimum height of the flag?

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

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 . How long does it take for the waterwheel to complete one turn?

Suppose that you want to model the height of a rider on a Ferris wheel as a function 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?

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds? Assume that right of center is a positive distance and left of center is a negative distance.