I'm currently working on the "cavendish" experiment and wish to use/develop a method separate from the casus we've been provided. Now I've nicely calculated and derived everything I need to know, including all the corrections that have to be made for the mass of the rod, the finite size of the masses, etc. However: I'm running in to a brick wall when it comes to finding a way to bring air resistance in to the picture.

For those of you don't know: The cavendish experiment is a torsion balance that is used to measure gravity. The way it works is by suspending a rod with some small masses on either end by a wire with low torsion spring coefficient. These small masses will start to move towards an equilibrium where the force supplied by the torsion in the wire and the force of gravity supplied by two larger masses brought in close proximity of the smaller masses cancel out.

The problem is that these small masses have a certain moment of inertia, so they'll end up oscillating about the position of equilibrium. This oscillation is of course dampened by air resistance. The most common way to go about finding the effect of air resistance is by setting up and solving a differential equation, which I prefer not to do. Because of this, I'm now looking in to alternative methods of (numerically) finding the way air resistance affects the period of the oscillation.

My work so far So far, I've determined that air resistance is irrelevant when determining the equilibrium position of the bar (which is used to determine $G$). Where air resistance does become relevant is in finding the value for $\kappa$ (torsion spring coefficient). Most of you will know that one can describe kappa with $\kappa=2m(\frac{\pi L}{T})^2$ where m is the point mass's mass and L the length of the rod. Because $T$ gets changed by friction, $\kappa$ can not be accurately determined without finding a way to go from $T_{measured}$ to $T_{frictionless}$. Herein lies my struggle, as I haven't been able to do so.

The reason I'm exploring this question of doing it without differential equations is in order to explore the science. I've got no problem actually working through the differential equation.