1. Second Order System (Continued)
A Pressure Transducer
ISAT 300
wk12B

2. Second Order Responses
Response of a 2nd-order System to a Sinusoidal Input
Amplitude Ratio (y/kxo)
Frequency Ratio (w/wn)
ISAT 300
wk12B

3. Pressure Transducer - An Example of 2nd-Order System
A small tube, 0.5 mm in diameter, is connected to a pressure transducer through a volume of 3.5 m3. The tube has a length of 7.5 cm. Air at 1 atm and 20oC is the pressure-transmitting fluid. Calculate the natural frequency for this system.
ISAT 300
wk12B

4. Pressure Transducer - An Example of 2nd-Order System
ISAT 300
wk12B

5. Pressure Transducer - An Example of 2nd-Order System
Calculate the damping ratio and the attenuation of a 100-Hz pressure signal in the system.
ISAT 300
wk12B

6. Cantilever Beam - Another Example of 2nd-Order System
A 1/16-in-diameter spring-steel rod is to be used for a vibration frequency measurement as shown in the figure below. The length of the rod may be varied between 1 and 4 in. The density of this material is 489 lbm/ft3, and the modulus of elasticity is 28.3106 psi. Calculate the range of frequencies that may be measured with this device.
ISAT 300
wk12B

7. Cantilever Beam - Another Example of 2nd-Order System=4
ISAT 300
wk12B

8. This Week in the Lab Measuring Parameters wd : the damped frequency
z : the damping ratio
wn : the undamped natural frequency
ISAT 300
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9. Measuring wd and z Measure the period and then calculate!
Find Values for yn and yn + k
Perform the following calculations:
Let:
 (Greek alphabet lambda)
Then find:
ISAT 300
wk12B

10. Measuring wn
After finding the previous two, the answer here is a simple calculation
ISAT 300
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11. The Solution Only Concerned with the underdamped response. ISAT 300
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12. The Solution
ISAT 300
wk12B