Modeling with Periodic Functions Answers

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?

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?

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?

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 equation models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance.

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.

Throughout the day, the depth of water at the end of a dock varies with the tides. The function represents the height, in feet, of the water t hours after midnight.Which graph shows the height of the water at the dock at any time after midnight?

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?

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t = 0 seconds. When the weight it released, it oscillates and returns to its original position at t = 3 seconds. Which of the following equations models the distance, d, of the weight from its equilibrium after t seconds?

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?

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?

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?

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.