Simple pendulum equation of motion

[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...

Homework Statement

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

Homework Equations

Equation of motion using Lagrange equiations.

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)

 

[Orodruin]

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.

 

[Nora Fajes]

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.

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!

 

[vela]

It really isn't very helpful if all you do is post your result. It's like someone saying, "My car doesn't work. What's wrong?"

There's a link to a LaTeX FAQ at the bottom of https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.635513/.

 

[Nora Fajes]

It really isn't very helpful if all you do is post your result. It's like someone saying, "My car doesn't work. What's wrong?"

There's a link to a LaTeX FAQ at the bottom of https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.635513/.

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.