The amplitude of vibration of a swing slowly decreased to ze

Solution

While swinging the potential energy is converted to kinetic energy and again kinetic energy is converted to potential energy. When the swing moves higher the potential energy increases and while moving back forth the kinetic energy increases. As, the swing moves higher, the potential energy of the swing also increases eventually. So, by pumping your legs the swing moves higher and potential energy is increased every time. When your legs are raised after pumping the center of mass of the system also raises which raises the height of the swing.

If we do not pump our legs the energy is lost in friction and swing slows down and comes to rest.