ENGE808-Advanced Measuring Systems Assignment 2026 | AUT

ENGE808-Advanced Measuring Systems

From Measurement Systems Application and Design (E. O. Doebelin) book:
Read Chapters 3, 4, and

Solve the following problems

1. In an analog-computer study it is desired to simulate a random atmospheric turbulence whose mean-square spectral density ∅𝑡(𝜔) is adequately represented as 10/(1 +.2), where 𝜔 is in radians per second. A white-noise generator having ∅𝑤𝑛(𝜔) = 10 is available. Select a suitable filter configuration and numerical values to follow the generator and produce the desired ∅𝑡(𝜔). The output of the noise generator should “see” a filter input resistance of 10,000 ohms.

2. Tests on a gyroscope show that it can withstand any random vibration along a given axis if the frequency content is between 0 and 1,000 rad/sec and the rms acceleration is less than 80 in./sec2. This gyro is to be mounted in a rocket where it will be subjected to acoustic-pressure-induced vibration. The transfer function between pressure and acceleration and the mean-square spectral density of pressure are as given in below figure 1. Will this gyro withstand the vibration?

3. The output of a potentiometer is to be read by a recorder of 10,000 ohms inputresistance. Nonlinearity must be held to 1 percent. A family of  potentiometers having a thermal rating of 5 watts and resistances ranging from 100 to 10,000 ohms in 100- ohm steps is available. Choose from this family the potentiometer that has the greatest possible sensitivity and also meets the other requirements. What is this sensitivity if the potentiometers are single-turn (360°) units?

4. What resolution is possible with a 60-turn wire-wound potentiometer using appropriate gearing?

5. In a Wheatstone bridge, leg 1 is an active strain gage of Advance alloy and 120 ohms resistance, leg 4 is a similar dummy gage for temperature compensation, and legs 2 and 3 are fixed 120-ohm resistors. The maximum gage current is to be 0.030 amp.

• What is the maximum permissible d-c bridge excitation voltage? (Use this value in the remaining parts of this problem.)
• If the active gage is on a steel member, what is the bridge output voltage per 1,000 psi of stress?
• If temperature compensation were not used, what bridge output would be caused by the active gage increasing temperature by 100°F if the gage is bonded to steel? What stress value would be represented by this voltage? Thermal-expansion coefficients of steel and Advance alloy are 6.5 × 10-6 and 14.9 × 10-6 in./(in.-°F), respectively. The temperature coefficient of resistance of Advance is 6 × 10-6 ohm/(ohm-°F).
• Compute the value of a shunt calibrating resistor that would give the same bridge output as 10,000-psi stress in a steel member.

6. Perform an analysis similar to that leading to Eq. (1), assuming output loaded with Rm, for the following:

• The circuit of Fig. 2a
• The circuit of Fig. 2b
• The circuit of Fig. 2c
• The circuit of Fig. 2d