"Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation."
A type of harmonic motion where the amplitude of oscillation decreases over time due to the presence of a dissipative force.
Simple Harmonic Motion: A description of the motion of an object subject to a restoring force proportional to its displacement from a fixed point.
Damped Simple Harmonic Motion: An extension of simple harmonic motion where the system is subject to a damping force that opposes the motion, leading to a reduction in amplitude over time.
Free Oscillations: Oscillations that occur without any external force acting on the system, in contrast to forced oscillations which occur in response to external forces.
Forced Oscillations: Oscillations that occur as a result of an external driving force.
Under-damped Oscillations: A type of damped oscillation where the damping force is less than critical, leading to oscillations that gradually decrease in amplitude.
Over-damped Oscillations: A type of damped oscillation where the damping force is greater than critical, leading to oscillations that quickly decay to equilibrium without oscillating.
Critical Damping: The minimum amount of damping required to eliminate oscillations without causing the system to over-damp.
Resonance: A phenomenon where the amplitude of oscillations is greatly enhanced when the driving frequency matches the natural frequency of the system.
Quality Factor: A measure of how well a system can sustain oscillations in the absence of external driving forces, defined as the ratio of the energy stored in the system to the energy lost per cycle.
Complex Exponential Form: A mathematical representation of damped oscillations in terms of complex exponentials, which allows for easy analysis of the behavior of the system.
Lagrangian Mechanics: A formalism for describing the motion of systems in terms of generalized coordinates and equations of motion, which can be used to derive the equations of motion for damped oscillators.
Electrical Analogs: A method for modeling damped oscillators using electrical circuits, which can aid in understanding the behavior of the system and allow for easier experimental verification.
Nonlinear Damping: An extension of damped oscillations where the damping force is not proportional to velocity, leading to more complex behavior such as periodic motion and chaos.
Underdamped Oscillations: In an underdamped oscillation, the system is able to oscillate back and forth with some decay, but the amplitude of each successive oscillation is smaller than the previous one. This result is due to the damping force that is present in the system.
Overdamped Oscillations: Overdamped oscillations occur when the damping force is greater than the critical damping value for the given system. This results in a system that is unable to oscillate and instead, moves slowly towards equilibrium.
Critically Damped Oscillations: In the case of critically damped oscillations, the damping force in the system is exactly equal to the critical damping value. This results in a system that quickly moves towards equilibrium without any oscillation.
Forced Oscillations: Forced oscillations occur when an external force is applied to the system. This force can be periodic or non-periodic and can cause the system to oscillate with a frequency that is different from its natural frequency.
Self-excited Oscillations: Self-excited oscillations occur when a system is able to obtain energy from within itself and begin oscillating. A common example is the swinging of a pendulum where the initial push given to the pendulum provides energy to the system, allowing it to continue oscillating.
Transient Oscillations: Transient oscillations are oscillations that occur only during the initial period of time after the system is initiated. These oscillations eventually decay and the system approaches equilibrium.
Damped Harmonic Oscillations: Damped harmonic oscillations are systems that undergo simple harmonic motion with damping. This means that the system oscillates back and forth with decreasing amplitude over time.
Envelope Oscillations: Envelope oscillations occur when a smaller, high-frequency oscillation is present on top of a larger, low-frequency oscillation. The high-frequency oscillation is termed as the envelope, while the low-frequency oscillation is referred to as the carrier.
"Damping is produced by processes that dissipate the energy stored in the oscillation. Examples include viscous drag in mechanical systems."
"Damping is produced by resistance in electronic oscillators."
"Damping is produced by absorption and scattering of light in optical oscillators."
"Damping not based on energy loss can be important in other oscillating systems such as those that occur in biological systems and bikes (ex. Suspension (mechanics))."
"Not to be confused with friction, which is a dissipative force acting on a system. Friction can cause or be a factor of damping."
"The damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance."
"Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium."
"Losses (e.g. frictional) damp the system and can cause the oscillations to gradually decay in amplitude towards zero."
"The damping ratio is a measure describing how rapidly the oscillations decay from one bounce to the next."
"The damping ratio is a system parameter that can vary from undamped (ζ = 0), underdamped (ζ < 1), critically damped (ζ = 1), to overdamped (ζ > 1)."
"The behaviour of oscillating systems is often of interest in a diverse range of disciplines that include control engineering, chemical engineering, mechanical engineering, structural engineering, and electrical engineering."
"A normalised, or non-dimensionalised approach can be convenient in describing common aspects of behavior."