Modeling with Periodic Functions Answers

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.

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?

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.

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 height, h, in feet of a buoy in relation to sea level as a function of time, t, in seconds can be modeled by the graph below. How long does it take for the buoy to go from its highest point to its lowest point and then back to its highest point?

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?

Blood pressure can be modeled by a sinusoidal curve, where the maximum and minimum on the curve correlate to the person’s blood pressure reading. Henry’s blood pressure is modeled by the function , where t is time in seconds.Which graph accurately depicts this model?

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?

Mark sits on a swing that is 2.5 feet off the ground. Swinging as hard as he can, the swing reaches a height of 6 feet. Assuming Mark holds a steady pace, the height of the swing could be represented by a cosine curve.If Mark makes a full swing forward and backward in 3 seconds, which graph below could represent the height of the swing, in feet, for any time, t?

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?