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.

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

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?

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 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 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.

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, 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?