Help with damped pendulum problem

I have a problem for one of my classes in which I need to solve a damped pendulum problem. The equation is theta"+c/mLtheta'+g/L*sin(theta)=0. I have solved it using numerical methods (Runge-Kutta and Euler's Method) but I need an analytical solution so that I can find the error of these two methods. Can anyone help me?

You don't have a picture of it or something, do you? I can't read plain text problems worth a crap.

Maybe if you had a picture, unfortunately I think I'd only be able to figure it out using Eulers...

Miata.

I'm assuming you are given c, m, g and L..

If I recall my vibrations course correctly, that's a tough problem to do analytically. Maybe you can get away using the small angles approximation:

sin(theta) ~ theta

This gets rid of your sin theta term and should make things easier from there.

I assume it's the sin(theta) part that is making this difficult to solve. If it was just theta you could use substitution to solve it pretty easily but the sine screws things up. Can you just assume that sin(theta) = theta? (Edit: Hamburglar beat me to it). That works at small angles, but I don't know what your initial boundary conditions are so it might not apply. I'm guessing it won't though, and will introduce error into your attempt to quantify the error of your approximations.

Good luck with the problem, and post the solution when you get it please, hopefully it will stir up some of my long forgotten math skills.

Bob

I was given c, m, L, g. I am trying to find the error that the Euler's method and Runge-Kutta produce. I was using the equation (Analytical Solution-Numerical Solution)/(Analytical Solution). Does anyone know any other way to find the error?

Whats wrong with that way?

Agreed, that's the standard error formula...

How did this turn out?

I think he is asking for help with an analytical solution, not how to calculate the error.

I couldn't find the analytical solution. We end up calculating the error two ways; using error=f'(xi,yi)/2!+...+f'(xi,yi)^(n-1)/n!+O(h^(n+1)) and the small angle assumption.