00:01
In this problem, we've been told the amplitude, the frequency, and the maximum displacement is at t equals zero.
00:07
And we want to come up with a model equation for the simple harmonic motion.
00:13
So we have some formulas here that we need to know.
00:17
And because we are dealing with a maximum displacement, we're going to be dealing specifically with cosine because it starts at its maximum.
00:24
The amplitude is going to tell us what a is.
00:27
So we're going to go ahead and have three times the cosine.
00:31
We still don't know that coefficient here in front of the t, but we can find it because we have this formula.
00:37
We know that the frequency, w over 2 pi, is going to equal 1 over pi here.
00:44
So when we cross multiply, we get pi times w equals 2 pi, and dividing both sides by pi tells us that our coefficient here is 2.
00:52
So this is going to be our equation.
00:54
And then we're asked to do a rough sketch of this graph.
00:59
So if we do that, keeping in mind that the amplitude is 3, so we're going to be having a max up here at 3 and a min down here at negative 3...