The Torsion Pendulum

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Graphical Solution

Once the torsional stiffness and pendulum MOI are determined, the gun MOI equation may be plotted using a program like MS Excel to minimize the need for further calculations when measuring your guns. Here is an example of a graph for a pendulum having a torsional spring stiffness,          k = 0.382, and a pendulum MOI, Ip = 0.014.       Ig = k ( t / 2Pi )^2 - Ip Find the average period of the gun on the pendulum, t,  at the bottom of the graph.  Proceed straight up until you reach the purple line, and then go straight to the left edge to read the gun's MOI, Ig. For example, if the gun and pendulum have an average period of 4.08 seconds, the gun's MOI is 0.147 slug-ft^2.

Average Period, t, versus Gun MOI, Ig k = 0.382, Ip = 0.014 slug-ft^2