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The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping coefficient:
= is called the "damping ratio". Step response of a damped harmonic oscillator; curves are plotted for three values of μ = ω 1 = ω 0 √ 1 − ζ 2. Time is in units of the decay time τ = 1/(ζω 0). The value of the damping ratio ζ critically determines the behavior of the system. A damped harmonic oscillator can be:
Here damping ratio is always less than one. Critically damped A critically damped response is the response that reaches the steady-state value the fastest without being underdamped. It is related to critical points in the sense that it straddles the boundary of underdamped and overdamped responses. Here, the damping ratio is always equal to one.
The value that the damping coefficient must reach for critical damping in the mass-spring-damper model is: =. To characterize the amount of damping in a system a ratio called the damping ratio (also known as damping factor and % critical damping) is used. This damping ratio is just a ratio of the actual damping over the amount of damping ...
The damping force is proportional to the velocity of the object and is at the opposite direction of the motion so that the object slows down quickly. Specifically, when an object is damping , the damping force F {\displaystyle F} will be related to velocity v {\displaystyle v} by a coefficient c {\displaystyle c} : [ 2 ] [ 3 ]
Coulomb damping is a type of constant mechanical damping in which the system's kinetic energy is absorbed via sliding friction (the friction generated by the relative motion of two surfaces that press against each other). Coulomb damping is a common damping mechanism that occurs in machinery.
Classic model used for deriving the equations of a mass spring damper model. The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers.
Material damping or internal friction is characterized by the decay of the vibration amplitude of the sample in free vibration as the logarithmic decrement. The damping behaviour originates from anelastic processes occurring in a strained solid i.e. thermoelastic damping, magnetic damping, viscous damping, defect damping, ...