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!

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