Finding the Center of Mass of a Soft Spring

TL;DR

This paper derives a calculus-based method to determine the center of mass of a non-uniform, vertically suspended soft spring, accounting for gravity-induced stretching, providing a general expression for its vertical center of mass position.

Contribution

It introduces a novel calculus approach to find the center of mass of a non-uniform spring under gravity, which was not previously available.

Findings

Derived a general formula for the spring's center of mass

Accounted for non-uniform stretching due to gravity

Provided a practical method for analyzing soft springs' mass distribution

Abstract

This article shows how to use calculus to find the center of mass position of a soft cylindrical helical spring that is suspended vertically. The spring is non-uniformly stretched by the action of gravity. A general expression for the vertical position of the center of mass is obtained.