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I've been looking through my textbooks and I've found a number of different equations - so I wanted to confirm with you which it is.

What is the equation which determines the damping constant (gamma) in a spring executing shm?

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    It is an underdamped spring. Basically I'm trying to find the equation which will calculate the damping constant given the mass, spring constant, amplitude or whichever other variables are relevant. There are a variety of formulas in the link Sammy provided, basically I'd just like some confirmation as to which will find the 'damping constant' (ie the constant in the exponent of the decaying exponential equation of the damped motion).2011-05-06

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In the equation for the motion of a damped spring

$m\ddot{x} + c\dot{x} + kx = 0$

the parameter $c$ is known as the viscous damping coefficient. From it you can determine the damping ratio

$\zeta = \frac{c}{2\sqrt{mk}}$

which determines if the spring is underdamped ($\zeta<1$), overdamped (\zeta>1) or critically damped. The parameter $c$ itself is a property of the spring, and is not determined by $m$ or $k$.

You solve this equation by postulating a solution of the form $x(t)=e^{\gamma t}$, giving a quadratic equation for $\gamma$:

$m\gamma^2 + c\gamma + k = 0$

which you solve with the usual quadratic formula:

$\gamma_{\pm} = \frac{1}{2m} \left( -c \pm \sqrt{c^2 - 4mk} \right)$

giving two possible values for the decay constant. If $c^2<4mk$ then your spring is underdamped, and the rate of decay is given by the real part of $\gamma$, ie $\mathrm{Re}(\gamma) = -c/(2m)$.

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    What are the units of the damping constant? (by dimensional analysis of the equation)2011-05-07