Should damping ratio increase or decrease with increase in mass?

Question

I'm currently doing a small project in college for structures being damped. We're adding weights to a structure and measuring the damping affect. We've calculated the damping ratio and coeffecients, however, we currently have damping ratio increasing with mass, which I do not believe is correct following the below equation:

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

The above equation, assuming $k$ and $c$ are constant, suggests that $\zeta$ decreases as mass increases.

However, the results we are getting are entirely different, and we do not have a constant value for the damping coefficient:

We got the initial value of damping ratio by interpreting the graphs by using the following equation and process:

$${\sqrt{\frac{\left(\ln \left(\frac{x_n}{x_0}\right)\right)}{4(\pi n)^2+ \left(\ln \left(\frac{x_n}{x_0}\right)\right)}}} = \zeta$$

Where the above was rearranged from:

$$\Large{\frac{x_n}{x_0}= e^{\frac{-2\pi n \zeta }{\sqrt{1-\zeta^2}}}} $$

where $n=$ the number of full wave cycles between $x_0$ and $x_n$

Ultimately, I'm curious if the damping ratio should decrease with increase in mass, and should the damping coefficient stay constant?

Edit 2: Graphs for Unweighted vs 4.004 damping

Answer 1

I assume that your structure is a simple single spring mass damper system? For such a system the assumption of decreasing dampingratio $\zeta$ for increasing mass $m$ is correct. You need more dampingforce to stop a heavier system, therefore resulting in a smaller $\zeta$.

In reality though it could be that the additional mass affects the damping behaviour of your damper. There could be more reasons why your results don't fit the expectations. If you can supply some more information about your system it could be easier to pinpoint to the problem.

Edit1: Added image that shows the expected plot for different $\zeta$ values and different masses. The given data is flipped. My assumption are $c=2.5 kg/s$ and $k=162~kg/s^2$.