$14-$A certain pressure transducer acts as a second$-$order system. It has a natural frequency of n

$=50,000$rads $$and $=0\mathrm{.}8$and a static sensitivity of $0\mathrm{.}4$VkPa.

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$t$)$kPa$.$

Answer the following questions:

What is the amplitude of the transducer output $($in V$)?$

V

Now assume you know that the output amplitude of the pressure transducer is $0\mathrm{.}6$V$,$what is the

amplitude of the output of the filter $($in V$)?$