Question

I am trying to calculate the frequency response of a pressure transducer (PX302-030GV) which is usually a second-order system. How I can calculate the damping ratio of a second-order system if the frequency is 2000Hz (according to datasheet). Is it possible to calculate the frequency response using this transfer function?

H(s) = (w_{n} )^{2} / (s^{2}+
2*ζ*w_{n}*s+ w_{n}^{2}) Where,
w_{n}= natural frequency= 2*pi*f and f=2000Hz

ζ = damping ratio

Answer #1

As f =2000 Hz is known quantity, the undamped natural frequency
of oscillation w_{n} = ( 2* pi*f) is also known. The only
unknown quantity in the transfer function is the damping ratio.

If the system is fed with sinusoids of varying frequency using a function generator, the magnitude and the phase of the output can be obtained. For a particular input frequency w, we can find out the gain of the system and can compare that with the gain obtained from the transfer function for frequency w ( put s =jw in the transfer function) and can calculate the only unknown quantity in the system i.e the damping ratio of the system.

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