What are damped oscillations? Discuss them using the illustration of a spring.

(N/A) Damped oscillations: Oscillations in which the amplitude of the oscillator decreases with time are known as damped oscillations.
The motion of a simple pendulum swinging in air eventually dies out because air drag and friction at the support oppose the motion.
The mechanical energy of the oscillating system is dissipated as heat due to these resistive forces,causing the mechanical energy to decrease. According to the relation $E = \frac{1}{2} k A^2$,the amplitude $A$ gradually decreases.
Illustration with a spring:
Consider a block of mass $m$ connected to an elastic spring of spring constant $k$,oscillating vertically as shown in the figure. If the block is pushed down and released,it oscillates in a vertical plane with an angular frequency $\omega = \sqrt{\frac{k}{m}}$.
In practice,the surrounding medium (e.g.,air) exerts a damping force on the block,causing the mechanical energy of the block-spring system to decrease. This energy loss appears as heat in the surrounding medium and the block. The damping force depends on the nature of the medium; if the block is immersed in a liquid,the damping is much greater and energy dissipation is faster. The damping force is generally proportional to the velocity of the block.