The internal ballistics of a spring gun

We consider the features of pellet motion under the elastic force acting from a decompressing spring of a finite mass. The muzzle speed of the pellet decreases as the ratio between spring and pellet mass increases. In the general case, the pellet loses contact with the spring as it is stretched. This effect occurs due to the fact that the peak of elastic displacement wave, propagating from the fixed end, reaches the opposite end of the spring. With a large relative mass of the pellet, it accelerates along a quarter of the sinusoid. At the limit of a very small pellet mass, it moves nearly all the time along with the end of the spring at an almost constant speed, approximately equal to the speed of sound propagation in the spring. In this case, after the initial compression, the pellet passes the equilibrium position, and comes off after moving a similar distance beyond the equilibrium.