The maximum displacement from equilibrium of a ballistic pendulum is analyzed as a function of projectile mass. The displacement can be determined according to the conservation laws of energy and momentum, which are applied in three stages. For an ideal spring-gun, the pendulum's maximum displacement height should increase monotonically with the mass of the projectile until the mass of the projectile and the effective mass of the pendulum are equal, after which the displacement height decreases monotonically with projectile mass. The additional mass of the spring and driver mechanism shifts this peak towards higher projectile masses. This relationship was tested using a cup-catcher and a set of blocks of varying mass as the projectiles, and the pendulum maximum displacement does indeed increase with mass to a point before slowly decreasing.
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In Gupta's experiment, he measured the speed of the projectile by ranging the gun, and then determined the muzzle velocity of the projectile using the collisions with the pendulum. He supplies a table of values using a modified ballistic pendulum, but the first row of the table corresponds to the unmodified pendulum (e.g., the ballistic pendulum which is equivalent to that used in this paper). For this unmodified pendulum, he found an agreement to within 3% using linear momentum.
The specific ballistic pendulum used was the Sargent-Welch Ballistic Pendulum, Model 0870. This is a fairly old model, and the Sargent-Welch company no longer carries it in stock. As best as the author can ascertain, this model is most nearly like the Sargent-Welch/Llewellen Design Advanced Ballistic Pendulum, Sargent-Welch catalogue no. 470200-994.
