1. Use Simulink or any other software to determine the time response of the microphone with τ_l= τ = 1 sec, ω_n = 1500 Hz, ζ = 0.5 and K=2.5 due to the sonic boom pressure of FIGURE 6.47. Does this device give a good reproduction of the signal? Is this a practical microphone? Why?

2. If, in the system shown in Fig. 7.17, the amplifier tag is not neglected, so that (i/e_e) (D) = K_a/[(τ₁D + 1) (τ₂ D + 1)], find the value of K_a that will put the feedback system just on the margin of instability (use the Routh criterion). If τ = 0.001 s and τ₁ = τ₂ = 0.000001, what is the maximum allowable value of K_b K_a K_e/I_m for marginal stability? If a value of K_b K_a K_e/I_m about one-fifth of that giving marginal stability can be used and if Eq. (7.43) is assumed applicable under these conditions, what percentage improvement of τ_ct as compared with τ may he achieved?

The block diagram of Fig. 7.17 embodies the above relations, which may now be manipulated to give the relation between input v and output, e_o:

((K_ee_o/R_ro)+ Kv)((1/I_m)(-K_bK_aR_ro)/τD+1) = e_o              (7.41)

This gives finally

 e_o/v(D) = (K_ct/τ_ctD+1)                                                 (7.42)

where  τ_ct =^Δ  τ/1+ K_eK_bK_a/I_m                                      (7.43)

and K_ct =^Δ ((-KK_bK_aR_ro/I_m)/(1+K_eK_bK_a/I_m))                 (7.44)

3. Perform a dynamic analysis on the system of Fig, 7,47a to obtain the transfer function relating fluid density as an input to strain-gage bridge voltage as an output. What is the effect of changes in liquid level in the still well on the output signal? What is the effect of thermal (volume) expansion of the float? If the entire assembly is aboard a vehicle that is accelerating vertically, explain the effect on the output.

4. A thermometer is to have a sensitivity of 10 in/^oC when mercury is used in the neighborhood of room temperature. Obtain an expression relating capillary cross-section area and bulb volume to meet this requirement. Obtain expressions for the time constant if the bulb is spherical and, if it is cylindrical with a length equal to 5 diameters. Also find the ratio of these two time constants.

5. A resistance-thermometer circuit as in Fig. 8.21d has R₁ = R₂ = 1000 Ω and is to cover the temperature range 0 to 400^oC. The thermometer element is platinum with a resistance of 1,000 Ω at 200^oC. Plot the curve of bridge output voltage (open circuit) versus input temperature, using the data of Fig. 8.19. Sec Chap. 10 for bridge-circuit equations. Bridge excitation is 20 V.