Forced
oscillation
Damped
Harmonic Motion
mass-spring
system : 
The
magnitude of the frictional force usually depends on the speed.
Different
degrees of damping
1.
Underdamping
:
Amplitude decays exponentially
with time
2.
Critical
damping : The
system does not oscillate at all after
released but settles
directly back to its
equilibrium position and the time taken is
minimum
3.
Overdamping
:
The system does not
oscillate at all but
takes the longest time to return to
its
equilibrium position.
Examples
of application of critical damping : shock absorbers in vehicles and
electrical meters
Forced
oscillation
The
equation of motion of the system is
The
general solution of the above differential equation is
where a(w) is a function of w
(
The above general solution may be neglected.
The
first part of the above solution is called transient
solution.
The
second part is called steady
state solution.
At
large t, the steady state solution is the only remaining and the system
oscillates with the frequency w of the driving force. )
Resonance
1.
If the external applied forced frequency is equal to the
natural frequency of the driven system,
resonance occurs.
2.
At resonance, energy transferred from the driving source to the
driven system is most effective and the amplitude is maximum.
Examples
of resonance
Barton’s
pendulum, Hacksaw blade oscillator, Kundt’s tube,
