Damping
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This article is about damped harmonic oscillators. For detailed mathematical description of the harmonic oscillator including forcing and damping, see Harmonic oscillator. For damping in music, see Damping (music). In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator. In mechanics, friction is one such damping effect. For many purposes the frictional force Ff can be modeled as being proportional to the velocity v of the object: Ff = cv, where c is the viscous damping coefficient, given in units of ne...
This article is about damped harmonic oscillators. For detailed mathematical description of the harmonic oscillator including forcing and damping, see Harmonic oscillator. For damping in music, see Damping (music). In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator. In mechanics, friction is one such damping effect. For many purposes the frictional force Ff can be modeled as being proportional to the velocity v of the object: Ff = cv, where c is the viscous damping coefficient, given in units of newton-seconds per meter. Generally, damped harmonic oscillators satisfy the second-order differential equation: frac{d^2x}{dt^2} + 2zetaomega_0frac{dx}{dt} + omega_0^2 x = 0, where 0 is the undamped angular frequency of the oscillator and is a constant called the damping ratio. For a mass on a spring having a spring constant k and a damping coefficient c, 0 = k/m and = c/2m 0.
