Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled 5 cm down from equilibrium and released. After 2 seconds the amplitude has decreased to 3 cm. Also, the spring oscillates 13 times each second. Assuming that the amplitude is decreasing exponentially, below is a model for the distance, D the end of the spring is below equilibrium, in terms of seconds, t: D(t) = 5(0.7746)* . cos(267rt) . [Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have negative values for D.] After t = 7 seconds, how far from equilibrium is the end of the spring? If your answer is a decimal, please round to no more than 3 decimal places.

Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled 5 cm down from equilibrium and released. After 2 seconds the amplitude has decreased to 3 cm. Also, the spring oscillates 13 times each second. Assuming that the amplitude is decreasing exponentially, below is a model for the distance, D the end of the spring is below equilibrium, in terms of seconds, t: D(t) = 5(0.7746)* . cos(267rt) . [Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have negative values for D.] After t = 7 seconds, how far from equilibrium is the end of the spring? If your answer is a decimal, please round to no more than 3 decimal places.