|
Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples include viscous drag in mechanical systems, resistance in electronic oscillators, and 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. The damping of a system can be described as being one of the following: ;Overdamped: The system returns (exponentially decays) to equilibrium without oscillating. ;Critically damped: The system returns to equilibrium as quickly as possible without oscillating. ;Underdamped: The system oscillates (at reduced frequency compared to the ''undamped'' case) with the amplitude gradually decreasing to zero. ;Undamped: The system oscillates at its natural resonant frequency (''ω''o). For example, consider a door that uses a spring to close the door once open. This can lead to any of the above types of damping depending on the strength of the damping. If the door is ''undamped'' it will swing back and forth forever at a particular resonant frequency. If it is ''underdamped'' it will swing back and forth with decreasing size of the swing until it comes to a stop. If it is ''critically damped'' then it will return to closed as quickly as possible without oscillating. Finally, if it is ''overdamped'' it will return to closed without oscillating but more slowly depending on how overdamped it is. Different levels of damping are desired for different types of systems. == Linear damping == A particularly mathematically useful type of damping is linear damping. Linear damping occurs when a potentially oscillatory variable is damped by an influence that opposes changes in it, in direct proportion to the instantaneous rate of change, velocity or time derivative, of the variable itself. In engineering applications it is often desirable to linearize non-linear drag forces. This may be done by finding an equivalent work coefficient in the case of harmonic forcing. In non-harmonic cases, restrictions on the speed may lead to accurate linearization. In physics and engineering, damping may be mathematically modeled as a force synchronous with the velocity of the object but opposite in direction to it. If such force is also proportional to the velocity, as for a simple mechanical viscous damper (dashpot), the force may be related to the velocity by : where ''c'' is the ''damping coefficient'', given in units of newton-seconds per meter. This force may be used as an approximation to the friction caused by drag and may be realized, for instance, using a dashpot. (This device uses the viscous drag of a fluid, such as oil, to provide a resistance that is related linearly to velocity.) Even when friction is related to , if the velocity is restricted to a small range, then this non-linear effect may be small. In such a situation, a linearized friction coefficient may be determined which produces little error. When including a restoring force (such as due to a spring) that is proportional to the displacement and in the opposite direction, and by setting the sum of these two forces equal to the mass of the object times its acceleration creates a second-order differential equation whose terms can be rearranged into the following form: : where ''ω''0 is the undamped angular frequency of the oscillator and ''ζ'' is a constant called the damping ratio. This equation is valid for many different oscillating systems, but with different formulas for the damping ratio and the undamped angular frequency. The value of the damping ratio ''ζ'' determines the behavior of the system such that ''ζ'' = 1 corresponds to being critically damped with larger values being overdamped and smaller values being underdamped. If ''ζ'' = 0, the system is undamped. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「damping」の詳細全文を読む スポンサード リンク
|