Reduction of the size of oscillations by the removal of energy. For example, the indicator needles of gauges are often immersed in oil to give frictional damping; and resistive circuit components reduce electrical oscillations.
Damping is any effect, either deliberately engendered or inherent to a system, that tends to reduce the amplitude of oscillations of an oscillatory system.
In playing stringed instruments such as guitar or violin, damping is the quieting or abrupt silencing of the strings after they have been sounded, by pressing with the edge of the palm, or other parts of the hand such as the fingers on one or more strings near the bridge of the instrument.
Example: mass-spring-damper
An ideal mass-spring-damper system with mass m (in kilograms), spring constant k (in newtons per meter) and damper constant B (in newton-seconds per meter) can be described with the following formula:
Treating the mass as a free body and applying Newton's second law, we have:
where a is the acceleration (in meters per second2) of the mass and x is the displacement (in meters) of the mass relative to a fixed point of reference.
Differential equation
The equations of motion combine to form a second-order differential equation for displacement x as a function of time t (in seconds):
Rearranging, we have
Next, to simplify the equation, we define the following parameters:
and
The first parameter, ω0, is called the (undamped) natural frequency of the system.
The differential equation now becomes
Continuing, we can solve the equation by assuming
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