Modeling with Periodic Functions Answers

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

Suppose that you want to model the height of a rider on a Ferris wheel as a function of time. The amplitude of the function you use as a model should be equal to which of the following?

Tides in a specific location can be approximated using the periodic function shown on the graph.What is the interpretation of the amplitude in this application?

The distance, d, in inches of a weight attached to a spring from its equilibrium as a function of time, t, in seconds can be modeled by the graph below. Which equation is represented in the graph below?

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, h, in feet of the tip of the minute hand of a wall clock as a function of time, t, in minutes can be modeled by the equation . Which number (from 1 to 12) is the minute hand pointing to at t = 0?

A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model h, the height in feet of the buoy in relation to sea level as a function of time, t, in seconds?

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.

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?

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?