U-tube manometer is first order system or second order system?

Answer:

U-tube manometer is  second order under damped system

What is under damped system?

Answer:  For a second order system the transfer function is in the below form

 Here if the

ζ < 1 system response is said to be Under damped or oscillatory.

 ζ =1 system response is said to be Critically damped .

ζ > 1 system response is said to be Over damped or non-oscillatory.