00:01
We'd like to find the magnitude of the damping force at unit speed for part a.
00:05
So let's begin.
00:08
Our damping frequency, or our natural frequency, omega -n, is the square root of gravity divided by x.
00:16
So sort of our displacement.
00:19
So in this problem, we're going to have our 9 .81, or if we convert this all to centimeters, 981 divided by 1 .8.
00:29
And so it's 23 .1 radiance per second.
00:34
But our amplitude reduces to one quarter, one quarter of its initial value, as told in our problem, into oscillations.
00:47
So if we have two oscillations, then it reduces to one quarter of that original value.
00:54
Or, let's just call this, yeah, x is fine.
00:59
Or this means that x over xn is equal to four.
01:07
So we can find our logarithmic, how much it decreases logarithmically.
01:14
We can call this delta equal to 1 over n log of x over xn.
01:21
So if we plug that in, we get 0 .693.
01:26
But our dampen ratio is equal to 2 pi times, what we're going to call this phi.
01:33
So phi is equal to 0 .693 divided by 2 pi, which is 0 .11...