Potential energy of pendulum in terms of displacement.

[Nuclearturtle]

Hi guys, I'm having troubles finding how to write the potential energy of a 1D pendulum down. In terms of displacement however. This should be easy and it is, but my professor had this nice "clean" solution whereas mine is really dreadfull, any help? :)

edit: Ok nvm guys. I was thinking I went crazy for not finding it, since I almost have my physics license. But my professor used a Taylor approximation, nothing to worry about.

 

[Nuclearturtle]

By the way this is not homework, just a serious question to try to solve coupled harmonic oscillators :(

 

[BruceW]

hi, turtle :) welcome to physicsforums

Do you still have a question about pendulums? I agree Taylor approximation is the way to go. (That's why they say 'for small angles'). Also, do you mean 2D pendulum. And what's a physics license?!

 

[Nuclearturtle]

I meant a 1D pendulum in the sense that it only oscilates in one (!) direction. Of course this could represent a real 3D pendulum oscillating along just one axis.

Concerning the physics license, I didn't know how to sai it right, I meant physics degree or something like that. Let's just say I'm studying physics! This being the reason why I was so concerned not finding this "easy" solution :)

Thx for offering help anyway!

 

[PJC01]

As a fellow scientist, I can understand your frustration in trying to find a clean solution for the potential energy of a 1D pendulum in terms of displacement. However, it is important to remember that there are often many different ways to approach a problem and it is not uncommon for different individuals to come up with different solutions.

In this case, it seems like your professor used a Taylor approximation to simplify the potential energy equation. While this may seem like a "cleaner" solution, it is important to keep in mind that both solutions are valid and can provide useful insights into the behavior of the pendulum.

Additionally, it is always helpful to discuss your approach with others and see if they have any suggestions for improvement. Collaboration and open-mindedness are key components of scientific research and can lead to new and innovative solutions.

I hope this helps alleviate some of your concerns and I wish you the best of luck in your studies. Keep up the good work!