What are damped oscillations?

(N/A) Damped oscillations are oscillations in which the amplitude of the oscillating system decreases over time due to the presence of dissipative forces,such as friction or air resistance.
In an ideal system,an oscillator would continue to vibrate indefinitely with constant amplitude. However,in real-world systems,energy is lost to the surroundings as heat or sound.
The equation of motion for a damped harmonic oscillator is given by $m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = 0$,where $m$ is the mass,$b$ is the damping constant,and $k$ is the spring constant.
As a result of these dissipative forces,the mechanical energy of the system gradually decreases,leading to the eventual cessation of motion.