One last question. So the equation I now have is:
E(t) = (1/2)m(Ldø/dt)^2 + mgL(1-cosø)
But this is the equation of energy for a pendulum, not a damped pendulum, right?
So would the equation of energy for a pendulum where energy is constantly being taken out of the system be:
E(t) =...
Is my problem converting angular velocity into linear velocity? Because dø/dt itself is angular velocity. The only thing I can find is people using conservation of energy to solve for the velocity v. Of course, if I did that my equations would just cancel out.
Ah I'm meeting with my professor at 1:30...I'm running out of time to get this energy equation right.
1) Awesome.
2) Sweetness.
3)http://www.kettering.edu/~drussell/Demos/Pendulum/Pendulum.gif
cosø = h/L --> h = L - Lcosø. --> L(1-cosø)
4) I'm really not certain. It's not x(t) =...
Yes, all I am trying to do is develop equations for E(t) and E'(t). I am not able to make small angle approximations, and while I know that I will not actually be able to solve the second order differential equation, I just want to set up the equations correctly and then go as far as I can.
Maybe I've been on the wrong track. After all, KE + PE = Total E. So I shouldn't be adding a new term, but subtracting from a current one.
I'm thinking that this resistive force, air resistance/random frictions in reality but that's unimportant in our theoretical model, must be subtracting...
1. Yes, I believe the energy of a damped pendulum will have additional contributions to the total energy of the system. I define cø' as some damping force proportional to angular velocity (ø'). C is simply a constant. I suppose its units would then have to be kg/s. Therefore, this force would do...
This may straddle more advanced physics, but I thought it leaned toward introductory.
Homework Statement
I have been told to find the net energy of a damped pendulum.
Homework Equations
Obviously the equation of energy for an undamped pendulum is just:
E = KE + PE = .5mv^2 + mgh = 0
I...