# How does damping coefficient vary with mass? [closed]

Im going to be experimenting and I want top know what result I should get. This is basically what my graph is going to look like and it should help you get an idea of the experiment.

$$x(t)= x_0 e^{-\frac{c}{2m}}\cos (\omega t + \phi_0)$$

where c is damping coefficient

## closed as unclear what you're asking by Jon Custer, ZeroTheHero, Yashas, John Rennie, Kyle KanosMar 22 '17 at 10:18

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• We'd get a better idea for the experiment if you showed the damping coefficient somewhere or you made it more obvious what you mean. As is your question is extremely vague. – JMac Mar 21 '17 at 15:56
• @JMac this is basically all the background you need physics.stackexchange.com/questions/8495/… edit: ive forgotten how to use math jax sorry i added an equation – Adam apple Mar 21 '17 at 16:35
• It depends on what they're modelling I guess. If it's an ideal damper then no, it should have a set coefficient. If it's a real system where we are just modelling some real behaviour as a dampening coefficient, the mass may affect it depending on how it interacts with the system. – JMac Mar 21 '17 at 16:39
• It is usually under damping. So would damping coefficient decrease as mass increases @JMac – Adam apple Mar 21 '17 at 18:24
• First, define which of your symbols is the "damping coefficient." I know what I think a damping coefficient is, but I don't have any reason to know if you think the same! (And there are plenty of real-world situations involving damping where your graph is not the response you would expect). – alephzero Mar 21 '17 at 18:35

No, the damping coefficient will not vary with mass.

Based on the back in forth in the comments, you are confusing a few concepts here.

The damping coefficient (subscript $c$) is a measure of applied force compared to velocity. In terms of the equations of simple harmonic motion, this is a constant which has no terms dictated by mass.

Your mention of "under-damping" in the comments leads me to believe you are confusing damping coefficient $c$ with damping ratio $\zeta$.

$\zeta$ will determine the characteristics of the damped harmonic motion (i.e. under-damped, over-damped, critically damped). $\zeta$ is given by the equation $$\zeta = \frac{c}{2 \sqrt {mk}}$$ where $c$, $m$ and $k$ are all constants.

You can see that mass will absolutely affect the damping ratio, but not the damping coefficient (since that is assumed constant).

In a real life scenario the damper may not perform the same if different masses are used; but traditionally with the idealized equations it just has a constant value.

I find the Wikipedia page has some good information on harmonic oscillation. Also, if I misunderstood what your question was really about please let me know.

• I was originally talking about damping coefficient but as it is not dependent on mass and wont change i can look at how mass affects the damping ratio. MANY THANKS! im sorry about being vague my understanding is not great of this topic! – Adam apple Mar 21 '17 at 19:30