00:01
We'd like to find the value of this function, and alpha, beta, c1, and c2.
00:06
So we're given that our mass of our spring is equal to 10 kilograms.
00:13
Our damping constant, c, is 11.
00:15
Our stretch length is negative 1 .5 meters, and our force required is 3 newtons.
00:22
So for a spring, our force of our spring is negative kx.
00:27
So k is equal to negative 3 divided by the.
00:32
Negative 1 .5 so k is just equal to 2 so our value of c squared minus 4m k plugging in our values is equal to 41 meter squared kilogram squared per second squared now we want to find our position of mass after a few seconds we need to satisfy our differential equation 10 d2x d t squared plus 11 d x d t plus 2x is equal to 0.
01:09
So for our general solution, we have our solutions, d is equal to negative 0 .87 and negative 0 .23.
01:21
Now we can rewrite our general expression here.
01:25
We then have x of t is equal to c1, e to the negative 0 .87t, plus c2, e to the negative 0 .23t...
