EIT Dynamics and Vibrations 5 — Questions and Answers
Question 1: For an undamped spring-mass system under harmonic excitation, at what frequency ratio r = ω/ω_n does resonance occur?
- r = 0
- r = 0.707
- r = 1.0 (Correct answer)
- r = 1.414
Correct answer: r = 1.0
Resonance in an undamped system occurs when the excitation frequency equals the natural frequency, i.e., r = 1.
Question 2: For a damped system with ζ = 0.5, which category of damping applies?
- Underdamped (Correct answer)
- Critically damped
- Overdamped
- Undamped
Correct answer: Underdamped
A damping ratio 0 < ζ < 1 defines underdamped behavior, regardless of its exact value.
Question 3: A rotating machine has total mass 10 kg, eccentricity e = 0.01 m, and runs at ω = 100 rad/s. What is the imbalance force?
- 10 N
- 100 N
- 1000 N (Correct answer)
- 10000 N
Correct answer: 1000 N
F = meω² = 10 × 0.01 × 100² = 1000 N.
Question 4: For a viscously damped forced vibration system, the peak steady-state amplitude occurs at what frequency ratio?
- r = 1 always
- r = √(1 − 2ζ²) (Correct answer)
- r = √(1 + 2ζ²)
- r = 1/(1 − ζ²)
Correct answer: r = √(1 − 2ζ²)
The resonant peak in displacement occurs at r = √(1 − 2ζ²), which is slightly below 1 for underdamped systems.
Question 5: A vibration isolator transmits 10% of the applied force to its foundation. What is its transmissibility ratio?
- 0.01
- 0.10 (Correct answer)
- 0.90
- 10.0
Correct answer: 0.10
Transmissibility TR is the fraction of force transmitted; 10% = 0.10.
Question 6: A two-degree-of-freedom spring-mass system has how many natural frequencies?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
An n-DOF system always has exactly n natural frequencies (and mode shapes).
Question 7: For vibration isolation to be effective (TR < 1) in an undamped system, the frequency ratio r = ω/ω_n must satisfy:
- r < 1
- r = 1
- r > √2 (Correct answer)
- r > 2
Correct answer: r > √2
For an undamped isolator, TR = 1/|1 − r²| < 1 only when r > √2 ≈ 1.414.
EIT Dynamics and Vibrations 5
For an undamped spring-mass system under harmonic excitation, at what frequency ratio r = ω/ω_n does resonance occur?