A mass suspended on a spring will exhibit sinusoidal motion when it moves. If the mass on a spring is 85 cm off the ground at its highest position and 41 cm off the ground at its lowest position and takes 3.0 s to go from the top to the bottom and back again, determine an equation to model the data.

Question

anonymous · Answer

"85 cm off the ground at its highest position and 41 cm off the ground at its lowest position"

Find the average of these numbers to get the middle position.

That will be our amplitude.

"takes 3.0 s to go from the top to the bottom and back again"

this is saying the period is 3.0 s

anonymous · Answer

"sinusoidal motion"
Means our equation is in the form: $$
s(t) = a +b\sin(ct)
$$You need to find $a$ $b$ and $c$.

anonymous · Answer

Ooops... our amplitude won't be the average, it will be  half the difference.

kainui · Answer

I think drawing a picture of the spring would also help. Draw a picture whenever possible and label things moeen.

Also, the average is equal to half the difference. ;P

anonymous · Answer

The average is half the sum.

kainui · Answer

Wait, not exactly lol.

kainui · Answer

the average minus the smaller distance is half the difference.

anonymous · Answer

yeah, which is the amplitude we want... I make too many stupid mistakes sometimes.

kainui · Answer

Anyways, sorry to interrupt haha.

anonymous · Answer

so the equation that models this is a(t) = a + bsin (ct) correct?