Using θ'' -3θ = -100, the solution I get is
θ(t)=-22.44e-√3t - 10.893e√3t + 100/3
This fits with what I had expected to happen to the rotating body. So is this correct?
Using this website
http://www.wolframalpha.com/widgets/view.jsp?id=17adb9cfd6c67a920240e6db6fd8e8a1
y''-3y'+0y = 100
y(0)=0
y'(0)=20
The solution is
y = 1/9 (-300x+160e^3x -151)
Not the same as my solution. Taking this solution as correct, the graph of y versus x shows the exponential increase...
It seems that I have a second order non-homogenous differential equation with initial values.
The videos seem to have equations of the form
Ay'' +By' + Cy = f(x)
Mine is
y'' - 3y' = 100
I've found the first part of the solution to be
y= -20/3 + 20/3 e^3x
and the particular solution to be...
No, I don't know how to do that. I've taken a brief look on youtube and there are a lot of videos there on how to solve differential equations. So far, I haven't found one similar to this equation. I'll keep looking. Thanks very much.
Equation: angular acceleration = 3 (angular displacement) - 100
At start, when displacement is 0, the initial angular velocity is 20 rad per second clockwise.
I expect that the (-100) term will cause the angular velocity to decrease to 0 but since displacement is increasing during this process...