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# Differential Equation banter watch

1. (Original post by Gome44)
While the normal pendulum equation is solvable with elliptic integrals, the quadratically damped pendulum is not unfortunately.

Only numerical methods can be used to evaluate t at certain theta (incidentally I took this from one of my Matlab projects)
Oh :0

My bad. I used Runge-Kutta for both in my program anyway.
2. (Original post by Gome44)
You have the differential equation below. Prove the thing next to that. I can't do it so don't ask me for help, have fun xx

Edit: I now know how to do it. Alas, I still will not help to be evil
This is fun. Let's see if we can get started. First of all, let . Then we're going to look at

If you crunch through this for a bit, you'll get something like

which looks not too unpleasant. Who wants to take it up from here?
3. (Original post by Gregorius)
This is fun. Let's see if we can get started. First of all, let . Then we're going to look at

If you crunch through this for a bit, you'll get something like

which looks not too unpleasant. Who wants to take it up from here?
This is a really good idea. That's why I made it in post 4

But on a more serious note: what are the initial conditions?
4. (Original post by Gome44)
Not the way I've been told to do it, but it looks like that would work
5. (Original post by atsruser)
Actually I've just tried my method and it is essentially the same, just a different substitution (v= exp(-theta/2)w where v=d(theta)/dt).
6. (Original post by atsruser)
This is a really good idea. That's why I made it in post 4
Doh! Sorry.
7. (Original post by Gregorius)
Doh! Sorry.
I was hiding my light under a spoiler-shaped bushel which is why you missed my display of calculus-related brilliance, I guess.

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