System response magnitude ratios MA, MB, and M

3. Consider the following instrumentation scheme:
   Physical I x(t) system
   Instrument A: 2- order system
   vii

The instruments have the following characteristics:
In.trument B. 1 order s\ stern
z(t

Instrument A Instrument B Natural frequency OM 50 krad/s n/a Time constant t n/a 50 its Static sensitivity K 5mV 2mV/mV Damping ratio C 0.1 n/a Zero offset A 1.5 mV -2.5 mV
a. Determine analytically and plot the individual and total system response magnitude ratios MA, MB, and M, (w) versus frequency for the range 0 -100 krad/s b. If the steady-state input signal x(t) = 3sin( wt) + 2, with x unitless, t in seconds and w = 20 krad/s, determine the steady-state output signal z(t).

Sample Solution