EIT Dynamics and Vibrations 5

Question 1

For an undamped spring-mass system under harmonic excitation, at what frequency ratio r = ω/ω_n does resonance occur?

Accepted Answer

r = 1.0

Answer

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?

Accepted Answer

Underdamped

Answer

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?

Accepted Answer

1000 N

Answer

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?

Accepted Answer

r = √(1 − 2ζ²)

Answer

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?

Accepted Answer

0.10

Answer

Transmissibility TR is the fraction of force transmitted; 10% = 0.10.

(EIT) Engineer In Training Certification Practice Test