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

Explanation:

As we know that the distance between maximum and minimum distance of the position will be equal to double of the amplitude.

So here we can say that

Since it took 2 second to reach the position of maximum length from its position of minimum length so here time period of motion will be

so here angular frequency is given as

now the equation of motion will be

here its mean position from ground is at 6 ft 9 inch above and it will oscillate about it with an amplitude of 7 inch with time period of 4 s

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day