Let’s take an example to understand what a damped simple harmonic motion is. The forces which dissipate the energy are generally frictional forces. But for a small damping, the oscillations remain approximately periodic. In the damped simple harmonic motion, the energy of the oscillator dissipates continuously. An example of a damped simple harmonic motion is a simple pendulum.
These periodic motions of gradually decreasing amplitude are damped simple harmonic motion. When the motion of an oscillator reduces due to an external force, the oscillator and its motion are damped.
