Question

The motion of a simple spring hanging from the ceiling can be modeled with a cosine function. The bottom of the spring has a maximum height of 7 feet 4 inches and a minimum height of 6 feet 2 inches from the floor. It takes 2 seconds for the spring to expand from its minimum length to its maximum length. What is a cosine function that models the spring’s length in inches above and below its average, resting position? Express the model as a function of time in seconds

Answer 1

answer choices

Answer 2

f(t) = A cos (w t)

where A is the amplitude and W = 2π/T
I don't know how to do maths with feet and inches so im converting it to centimeters.


7 feet 4 inches = 223.52 centimeters
6 feet 2 inches = 187.96 centimeters

So for its resting position (assuming there's no mass) we have

(223.52 - 187.96 )/2 = 17.78 cm = 7 inches


Here you have the amplitude (A=7)


Now, the period is the time it takes to go from its maximum position to its maximum position, which is going to be twice the time it takes to go from its maximum to its minimum, so we know that the period is 2*2 and thus W = 2π/4 = π/2


f(t) = 7cos(π/2 t)

Answer 3

thnx so much