00:01
All right, so we have a spring undergoing simple harmonic motion.
00:05
And we're told that the equation for the harmonic motion is a sine omega t plus phi.
00:12
And we're told the amplitude is 0 .32 meters.
00:16
The initial position is negative 7 centimeters, basically 7 centimeters to the left of the origin.
00:23
And the velocity is negative 2 meters a second initially.
00:26
And then it has a total energy of 5 .6 joules.
00:32
And so we want to find the, first off, we want to find the phase constant.
00:39
And so we can do this by basically looking at what is x0.
00:44
This is negative 0 .07 meters.
00:47
And this should be equal to 0 .32 meters times the sign of our phase angle.
00:54
But that's not going to tell us what quadrant the phase angle is in.
00:57
And so, you know, there's, we could shift this by 90 degrees, for instance, and it'll remain the same if it's in the upper quad, or 45 degrees, excuse me.
01:08
And it'll remain the same.
01:11
So we kind of need to know what's the difference there.
01:14
But we can use the fact that the initial velocity is negative two meters a second.
01:21
And at t equals zero, this should be equal to the angular frequency times the amplification.
01:28
So times 0 .32 meters times the cosine of this phase angle.
01:34
Now we don't know the angular velocity yet, and that's what part two asks us to find.
01:39
But we can, to make things easier, let's go ahead and find that first.
01:42
So what we have is the total energy is 5 .6 joules.
01:46
And this should be, you know, the total energy should be when the amplitude is maximized, or when the displacement is equal to the amplitude...