Determine the natural frequencies experimentally

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Natural frequencies and damping ratios can be determined experimentally through forced vibration methods. One effective approach involves measuring the phase angle using a Bode plot, where a 90-degree phase shift indicates the natural frequency. Alternatively, a simpler method is to apply a known forced displacement and analyze the system's ring down to calculate the fundamental frequency and damping ratio in the time domain. Clarification on the system type, whether it is a mass-spring-damper or motorized system, can enhance the accuracy of the analysis. Understanding the specific system characteristics is crucial for selecting the appropriate measurement technique.
Mohamed_Wael
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How can we determine the system properties (natural frequencies & damping ratio ) practically using forced vibration?
One way is to measure the phase angle, using the bode plot, the exciting frequency corresponding to 90 (deg) phase shift should be the natural frequency, are there any other approaches using forced vibration as well?
 
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Do you have a forcing mechanism with displacement sensor for the output? (e.g. shaker table?)

If not, a quick and dirty method is to excite the system with a known/repeatable forced displacement, then watch the ring down to calculate the fundamental frequency (counting peaks and calculating period) and damping ratio in the time domain.

Maybe I have interpreted your system wrongly, is this a mass spring damper system, or a motorized system? Maybe describe what it is.
 
My idea is that I want to use immerse Whitetail Antlers in a fishtank to measure their volumetric displacement (the Boone and Crockett system is the current record measurement standard to place in a juxtaposition with) I would use some sight glass plumbed into the side of the tank to get the change in height so that I can multiply by the tank cross-section. Simple Idea. But... Is there a simple mechanical way to amplify the height in the sight glass to increase measurement precision...

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