Hello there. I'm currently dead beat on this problem, maybe because I'm not sure I quite understand what it's asking (I'm taking my upper level mechanics course in germany, and I don't have any books, and it's the second week, and I'm up at 4am with 2 problem sets due tomorrow, each half done. ahhh!)(adsbygoogle = window.adsbygoogle || []).push({});

Anyway, here's what I interpret:

A pendulum of length L and mass M is in a Gravitationalfield, where it is displaced by a small angle, theta and is lightly nudged. The displacement r is small in comparison to the length, L (r << L). Here, let the motion be treated in the horizontal plane.

a) What are the equations of motion in cartesian coordinates? (hinte: write the gravitational forces on the mass in spherical coordinates, then use the approximation r <<L)

These equations of motion are equivalent to which already known problems?

b) Show that the mass traces out an elliptical pth. Solve here the equations of motion.

I'm lost. I've been working on these sets all day (and since Tuesday, when I had another one due), and I'm just.. my brain is fried.

Any help would be appreciated!!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spherical pendulum, linear approximation?

**Physics Forums | Science Articles, Homework Help, Discussion**