Abstract
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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