Damped harmonic oscillation is a type of motion where an object moves back and forth, but its amplitude gradually decreases over time due to the presence of a damping force.

Imagine a spring attached to a weight that is free to move up and down. When the weight is pulled down and released, it will oscillate up and down due to the spring’s restoring force. However, if there is air resistance or friction present, the motion will gradually slow down and eventually come to a stop. This is an example of damped harmonic oscillation.

Here is an animation to help visualize this concept:

In this animation, the blue line represents the position of the weight over time. At the beginning, the weight oscillates up and down with a large amplitude. However, as time goes on, the amplitude decreases due to the damping force. Eventually, the weight comes to a stop at the equilibrium position.