Tag: free, forced and damped oscillations

Whenever there is a damping force, it will slow down the motion of a pendulum, and ultimately it will make the pendulum stop. This phenomenon is called damping.

The pendulum on its motion has friction particle. As a result of this frictional force slows down.

In case of dumped vibrations amplitude of oscillation gradually decreases with time.

It is our common experience that when a body is made to vibrate in a medium , the amplitude of the vibrating body continuously decreases with time and ultimately the body stops vibrating.this is called the damped vibrations.

Forced vibrations: External force is acting on the body. 
Free vibration: Constant amplitude and no external force.
Damped vibration: Amplitude is not constant, it keeps on decreasing due to environmental factors of the system like air resistance.  
Therefore, correct option is C. 

Any oscillation in which the amplitude of the oscillating quantity decreases with time is termed as damped oscilaation

In damped oscillations, the relation of amplitude of oscillations with time is given by $y={ y } _{ o }{ e }^{ -bt }=\frac { { y } _{ o } }{ { e }^{ -bt } } $, where
${ y } _{ o }=$ initial amplitude of oscillation
$t=$time
$b=$damping constant
since $b>0\quad & \quad t>0;$
${ e }^{ bt }>1\ { \Rightarrow e }^{ -bt }<1\ { \Rightarrow { y } _{ o }e }^{ -bt }<{ y } _{ o }\ \Rightarrow y<{ y } _{ o }$
which means that as the time progress, its amplitude will decrease.