A pressure transducer works as shown cartoon below: a pressure tap is connected through a

pressure line to the transducer, also called a sensor$,$ which includes a cavity and bellows. Higher

pressure in the fluid causes the bellows to deflect. This movement is converted into an electrical

signal.

This pressure transducer system has the response shown in the plot below to a step change in

pressure. Time in seconds is shown on the abscissa$.$ The response appears to be second order.

a$)$ Explain from the physics of the device

why a second order response might be

expected. You may assume that the

conversion of the deflection of the

bellows to an electrical signal is perfect;

that is$,$ zero order.

b$)$ From the data, determine the following quantities:

rise time

overshoot

settling time

period of oscillation

c$)$ Write a transfer function for the sensor

d$)$ What is the differential equations that could be used to model the system? Infer this from the

transfer function unless you want to model the physical system directly.

e$)$ Comment on whether this sensor$-$system be appropriate for operating the following systems:

Large power plant

Pressure for fuel injector of an internal combustion engine