I'm a highschool student investigating the damping of an oscillating structure by a pendulum mass damper. The structure has an accelerometer at the top to measure the acceleration. Although I know it is not completely true, I assumed that the pendulum always acted as a harmonic oscillator and tuned its natural frequency to that of the building. To increase the damping in the system, I tighten the screw that holds the pendulum and allows it to oscillate.
If I tighten the screw just enough I get a signal like this:
And I can actually model it and get the decay constant and from that get the damping ratio. I could also use logarithmic decrement to get the damping ratio. So far so fine.
However if I loosen the screw completely, it leads to a signal like this:
For which I can derive no model (no decay constant) nor can use logarithmic decrement since consecutive peaks clearly vary erratically. However, we can see that the signal decays at some point, and I would be very sure that it does so exponetially but not as orderly as with the first graph. How could I calculate the damping ratio for this case?
This is another signal I got for a less loosend screw:
But the story repeats
Any Ideas?? I had the intuition I could use somehting like the kinetice energy or maximum amplitude of each signal to infer the damping ratio but they are just intuitions, no developed ideas really.
p.d. I know that usually the damping ratio is calculated with displacement / time data but the damping ratio would be the same if I use acceleration data to calculate it, right?