Determine the natural frequencies experimentally

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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.