Free and Forced vibration of distributed mass system:
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Free and forced vibration of continuous systems. Emphasis. where ρ is the mass per unit length of the string. For small distributed-parameter models.Review of linear single degree of freedom system free vibration is carried out. Introduction.
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Answer:
Free vibrations: A body capable of vibrations is
said to perform free vibrations when it is disturbed
from its equilibrium position and left to itself.
In the absence of dissipative forces such as fric-
tion due to surronding air and intemal forces, the
total energy and hence the amplitude of vibrations
of the body remains constant. The frequencies of the
free vibrations of a body are called its natural
frequencies and depend on the body itself.
In the absence or a maintainin5 torce, in Practice,
the total energy and hence the amplitude decreases
due to dissipative forces and the vibration is said to
be damped. The frequency of damped vibrations is
less than the natural frequency.
2) Forced vibrations : The vibrations of a body in
response to an external periodic force are called
forced vibrations.
The external force supplies the necessary energY
to make up for the dissipative losses. The frequeney
of the forced vibrations is equal to the frequency of
the external penodic torce.
The amplitude of the forced vibrations depends
upon the mass of the vibrating body, the amplitude
of the external force, the difference between the
natural frequency and the frequency of the periodic
force, and the extent of damping.