00:01
We have this kind of a cylinder, so it's kind of a damping mechanism.
00:10
And so what we have is like an oil in here and then we have little holes through this plunger that as we push it down, it squeezes that oil through there.
00:20
And what that means is that this force here is proportional to the velocity and just because of the fluid analysis and the drag and the friction between the pore.
00:33
The pours and the oil, you know, this plunger and the oil.
00:38
So, you know, we have this pour and we have oil flowing through it, and there's, you know, obviously friction there.
00:44
And so it turns out that, you know, a good model for that is simply that this force is proportional to the velocity of this plunger, or basically the velocity of fluid that you're flowing, you're forcing through these holes.
01:01
And we use the proportionality.
01:03
Constant k now we have what they want let's see they want us to show that if we start from at t equals zero and x equals zero and we push this down that the equation relating these is the right is the position is linear in each of these variables.
01:32
So what we want to show is that the equation for x, you know, x as a function of p, t, time, and the velocity v, that it's linear in all of those.
01:48
So what we can do then is just say, well now you know a is dvv, v t, we divide through by m, again separate variables, and again we can integrate this with a change of variables.
02:03
This just goes, this is just t.
02:06
And we can see then that minus m over k times a natural log of p minus kb over p is t...