A certain pressure transducer acts as a second$-$order system. It has a natural frequency of n $=50,000$ rad$/$ s and $=0\mathrm{.}8$ and a static sensitivity of $0\mathrm{.}4$ V$/$kPa$.$

The output of this sensor is connected to a passive $3$rd order low$-$pass filter with a fc $=1$ kHz$.$ The input signal to the pressure transducer is P$=2$sin$(2$$2500$t$)$P$=2$sin$(2$$2500$t$)$ kPa.