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
Noah G
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!

Related questions
Impact of this question
2013 views around the world
You can reuse this answer
Creative Commons License