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
Mathematics
katieb

Answer 1

Your answer would be 7 cos(π/2 t)

Answer 2

Answer:

$y=7" cos \frac{\pi t}{2}$

Step-by-step explanation:

Givn that 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.

Middle line = average of 7'4" amd 6'2"

=6'9"

Amplitude = 7'4"-6;9"

= 7"

Hence the corresponding cosine function would be

$y=7" cos \frac{\pi t}{2}$