The period (the time it takes for one oscillation) of the gun and cradle is dependent on three variables:
1. The gun's MOI
2. The pendulum's MOI (it has its own mass, and, therefore, MOI)
3. The stiffness of the torsion spring
If we replace the gun with an object for which we already know its MOI, we can eliminate the first variable. But, we are still left with two unknowns.
If we can setup the mathematical solution with two sets of conditions, we can form a system of two equations having two unknowns, allowing us to solve for the unknowns.
For the first set of conditions, I use a calibration bar made from a piece of drill rod. Because of its uniform shape, its MOI may be calculated using a standard engineering formula. See the mathematical solution for details.
The calibration bar is placed on the pendulum and its average period of oscillation is determined and recorded.
The second set of conditions is established by measuring the average period of the empty pendulum.
Using the equations given in the mathematical solutions section, the pendulum's MOI and the spring stiffness are calculated and recorded for later use in determining a gun's MOI.
Once calibrated, the device may be disassembled, re-assembled and used for future measurements without re-calibrating, provided the spring is positioned so that its length remains unchanged.
