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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:
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.
Damping capacity is a mechanical property of materials that measure a material's ability to dissipate elastic strain energy during mechanical vibration or wave propagation. When ranked according to damping capacity, materials may be roughly categorized as either high- or low-damping.
= 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:
However, the unitless damping factor (symbol ζ, zeta) is often a more useful measure, which is related to α by = . The special case of ζ = 1 is called critical damping and represents the case of a circuit that is just on the border of oscillation. It is the minimum damping that can be applied without causing oscillation.
For a single damped mass-spring system, the Q factor represents the effect of simplified viscous damping or drag, where the damping force or drag force is proportional to velocity. The formula for the Q factor is: Q = M k D , {\displaystyle Q={\frac {\sqrt {Mk}}{D}},\,} where M is the mass, k is the spring constant, and D is the damping ...
Analysis shows that there are well-damped critical speed at lower speed range. Another critical speed at mode 4 is observed at 7810 rpm (130 Hz) in dangerous vicinity of nominal shaft speed, but it has 30% damping - enough to safely ignore it. Analytically computed values of eigenfrequencies as a function of the shaft's rotation speed.
Damping dissipates energy in the system, which reduces the vibration level which is transmitted at the natural frequency. The fluid in automotive shock absorbers is a kind of damper, as is the inherent damping in elastomeric (rubber) engine mounts. Damping is used in passive isolators to reduce the amount of amplification at the natural frequency.