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 / (s²+ 2*ζ*w_n*s+ w_n²) 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.