Tag: free, forced and damped oscillations

$\dfrac {1}{\sqrt {2}} = e^{-bt/m}$
$ln \sqrt {2} = \dfrac {bt}{m}$
$t = \dfrac {m}{b} \times \dfrac {1}{2} ln2$.

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 B. 

The tendency of one object to force another adjoining or interconnected object into vibrating motion is referred to as a forced oscillation.

When a periodically repetitive and oscillatory force acts on an object, then the object is forced to oscillate with the frequency of the periodic force. Such oscillation is known as forced oscillation. When an object is displaced from its mean position and allowed to vibrate along its mean position then the object vibrates with its own natural frequency. This is known as free vibration or oscillation. And an oscillation in which the amplitude goes on decreasing with time is known as damped oscillation.

By pushing a child on a swing a driving force is applied which forces the swing and the child in the forward direction. The gravitational force acts as a restoring force and pulls back the child to the original position. These two forces together set them into an oscillatory motion. By pushing the child the amplitude, that is the maximum displacement, increases.

The orbital motion of the earth around the sun is not an oscillatory motion as it is not a two and fro motion about a mean position. But it is a periodic motion.

Forced vibration is an action in which periodic repetitive and oscillatory force is applied on an object. In this condition, the object is forced to vibrate with the frequency of the applied force. Hence all are forced vibrations.

A motion of an unbalanced rotating component is an example of forced vibration. As to rotate it with the unbalanced condition some external agent is required.

Resonance is an example of forced oscillation.

In vibrating motion increase in amplitude results in increase in loudness.