# Simple pendulum equation of motion

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1. Oct 15, 2014

### Nora Fajes

Hi! I've been trying to find the equation of motion for the simple pendulum using x as the generalized coordinate (instead of the angle), but I haven't been able to get the right solution...

1. The problem statement, all variables and given/known data

The data is as usual, mass m, lenght l and gravity g. The X,Y axes origin can be anywhere I choose.

2. Relevant equations

Equation of motion using Lagrange equiations.

3. The attempt at a solution

This is the solution I'm supposed to find:

[x''+(x*x'^2)/sqrt(l^2-x^2)+(g*x*sqrt(l^2-x^2))/l^2]=0

(Sorry if it's a bit messy, I don't know how to type equations)

But I get other terms I can't get rid of and I don't know what I'm doing wrong... I'd appreciate any help! Thanks!

Edit: The extra term I get is (x'^2*x'')/sqrt(l^2-x^2) and also (2*g*x')/(sqrt(l^2-x^2)) instead of (g*x*sqrt(l^2-x^2))/l^2.

(Still don't know how to post equations)

Last edited: Oct 15, 2014
2. Oct 15, 2014

### Orodruin

Staff Emeritus
It would help if you actually showed us your attempt with the extra terms. Also, use of the homework template is mandatory, do not erease the template headings.

3. Oct 15, 2014

### Nora Fajes

Sorry about the template, already corrected that and also added my extra terms. I'm still trying to solve it (not just waiting for an answer here) so I'll update it if I get it right. Thank you!

4. Oct 15, 2014

### vela

Staff Emeritus
5. Oct 15, 2014

### Nora Fajes

Ok, this is what I've got so far (although you could've asked nicely), sorry it's in Spanish:

And the solution I need to get to:

Anyway, thank you for your help.