Vibrations & Waves
Damped Harmonic Motion
Mass-spring
system
General
solution
Specific
solution
Energy
of shm
Examples
of shm
Rotating
vectors
Molecular
vibrations
Introduction
Forces
General
solution
Steady state
solution
System
behaviour
Steady state
response
Steady state
example
Steady state
regimes
Energy
Resonance
examples
Introduction
Non
dispersive
media
Beats
Standing
waves
System
behaviour
Reflected
waves
Dispersive
media
Dispersion
examples
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Critical Damping
Critical Damping occurs when 
-
4
= 0 or Q = 1/2.
The equation of the motion is given by:
(see the maths)
where A and B are the two constants of integration. We may verify that this is indeed the equation of motion by substituting the
solution back into the equation of motion.
Light damping
A lightly damped system approaches equilibrium with a number of oscillations.
Heavy damping
A heavily damped system approaches equilibrium without oscillation but increasingly slowly as the damping increases.
Critical damping
A critically damped system approaches equilibrium as fast as possible without any overshoot or oscillation. This is a
very desirable attribute in many mechanical and electrical systems.
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