This study deals extensively with the constrained motion of a particle attached to one end of an elastic string and moving under the influence of different forces. It deals with a set of dynamic cases of this type of motion under different conditions such as horizontal motion on a horizontal surface (smooth, rough), vertical motion in a gravitational field under the influence of the resistance of the fluid in which the motion takes place, and two-dimensional motion (vertical-horizontal) in a gravitational field under the influence of an intermediate resistance perpendicular to the motion.