We have seen that the mechanical energy of a damped oscillator decreases in time as a result of the resistive force. It is possible to compensate for this energy decrease by applying an external force that does positive work on the system. At any instant, energy can be transferred into the system by an applied force that acts in the direction of motion of the oscillator. For example, a child on a swing can be kept in motion by appropriately timed “pushes.” The amplitude of motion remains constant if the energy input per cycle of motion exactly equals the decrease in mechanical energy in each cycle that results from resistive forces.

Key terms

• oscillation in which amplitude decreases in time.
• Under damped oscillation: with relatively low damping, the vibrating motion is preserved but the amplitude of vibration decreases in time
• Critically damped oscillation: the object returns rapidly to equilibrium after it’s released and doesn’t oscillate.
• Over damped oscillation: with relatively larger damping the piston returns to equilibrium without ever passing through the equilibrium point, but the time required to reach equilibrium is greater than in critical damping.