I've seen similar posts, but none in which a mass rotates vertically while connected to a spring, with gravity acting on the mass. I want to know if the path of the mass can be described algebraically or if an ODE with a single function exists. I've tried describing the problem with a differential equation, but did not get far because the velocity is not constant and the path is not circular.

I apologize if someone else has asked this question; I'm not too familiar with this site.

I've seen similar posts, but none in which a mass rotates vertically while connected to a spring, with gravity acting on the mass. I want to know if the path of the mass can be described with elementary functions or if an ODE with a single function exists. I've tried describing the problem with a differential equation, but did not get far because the velocity is not constant and the path is not circular.

I apologize if someone else has asked this question; I'm not too familiar with this site.