A spring attached to a ceiling is pulled down 20 cm. After 3 seconds, wherein it completes 6 full periods, the amplitude is 15 cm. Find a sinusoidal function modelling it's position t seconds after released?

1 Answer
Jan 16, 2018

h = 15cos(720t) - 20

Explanation:

We will want the independent variable to be time, t here, and the depended variable to be h, or height. We will make it a cosine function, because it starts at a maximum (we could also do a sine graph with a phase shift).

The period will be 3/6, or 0.5 seconds. This means the b-value will be 360/b = 0.5 -> b = 720

Given the amplitude is 15 cm, we get:

h = 15cos(720t) - 20

The vertical transformation will occur because of the 20 cm pulled down. Notice how I let the origin be the starting point for the unstretched spring.

Hopefully this helps!