Resonance
Forced vibration describes when one vibrating object forces
another to vibrate. The second object will vibrate with the
same frequencies as the first.
Every object has one or more natural frequencies based on
the object’s size, shape and composition. The natural
frequency is the frequency that requires minimum energy to
cause vibration.
If an object is forced to vibrate at different frequencies, a
large increase in amplitude will be seen at frequencies equal
to the object’s natural frequency – this phenomena is called
resonance.
In many situations resonance is desired (such as in radio or
microwave transmission and reception) and in many it is not
(such as in vibration of machinery and buildings).
Resonance is an amplification of the motion at a particular
frequency (called the resonant frequency)
At these frequencies, even small periodic driving forces can
produce large amplitude vibrations, because the system
stores vibrational energy.
To diminish the resonance at resonant frequency, the system
can be damped.
Resonance phenomena occur with all types of vibrations or
waves: there is mechanical resonance (cars and buildings,
quartz watches), acoustic resonance (vocal chords or musical
instruments), electromagnetic resonance (tuners of radio and
microwave circuits), nuclear magnetic resonance (NMR) (MRI
uses the same principle), optical resonance (laser cavity)
others.
Resonant systems can be used to generate vibrations of a
specific frequency (e.g. musical instruments), or pick out
specific frequencies from a complex vibration containing
many frequencies.
DAMPING
When damping is small, the resonant frequency is
approximately equal to the natural frequency of the system,
which is the frequency of free vibrations (and large
amplification).
In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory
system, particularly the harmonic oscillator.
In the mechanics, friction is one such damping effect. For many purposes the frictional force Ff can
be modeled as being proportional to the velocity v of the object.
The value of the damping ratio ζ critically determines the behavior of the system. A damped
harmonic oscillator can be:

Overdamped (ζ > 1): The system returns (exponentially decays) to equilibrium without
oscillating. Larger values of the damping ratio ζ return to equilibrium slower.

Critically damped (ζ = 1): The system returns to equilibrium as quickly as possible without
oscillating. This is often desired for the damping of systems such as doors.

Underdamped (ζ < 1): The system oscillates (with a slightly different frequency than the
undamped case) with the amplitude gradually decreasing to zero.
This force is an approximation to the friction caused by drag.
Example: mass-spring-damper
A mass attached to a spring and damper. The damping coefficient, usually c, is represented by B in
this case. The F in the diagram denotes an external force, which this example does not include.
Dependence of the system behavior on the value of the damping ratio ζ, for under-damped,
critically-damped, over-damped, and undamped cases, for zero-velocity initial condition.
The behavior of the system depends on the relative values of the two fundamental parameters, the
natural frequency ω0 and the damping ratio ζ.
In music
Guitar
On guitar, damping (also referred to as choking) is a technique where, shortly after playing the
strings, the sound is reduced by pressing the right hand palm against the strings, right hand
damping (including Palm muting), or relaxing the left hand fingers' pressure on the strings, left
hand damping (or Left-hand muting). Scratching is where the strings are played while damped, ie,
the strings are damped before playing. The term presumably refers to the clunky sound produced. In
funk music this is often done over a sixteenth note pattern with occasional sixteenths undamped.
Damping is possible on other string instruments by halting the vibration of the strings using the left
hand, similar to on a guitar.
Piano
On a piano, damping is controlled by the sustain pedal and the key dampers, with the strings being
damped unless the pedal and/or the respective key is pressed.
Gamelan
Damping is also important in most percussion instruments in the gamelan, including sarons, gendérs,
and gangsas. On instruments that are played with a single mallet, the left hand is used to damp the
previously hit note when a new note is played. On the gendér, which is played with mallets in both
hands, the keys must be damped by the same hand, and it requires practice to master the technique.
DAMPING SIMULATION