Dynamics and Vibrations Flashcards

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

Answer: r = 1.0

Resonance in an undamped system occurs when the excitation frequency equals the natural frequency, i.e., r = 1.

For a damped system with ζ = 0.5, which category of damping applies?

Answer: Underdamped

A damping ratio 0 < ζ < 1 defines underdamped behavior, regardless of its exact value.

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?

Answer: 1000 N

F = meω² = 10 × 0.01 × 100² = 1000 N.

For a viscously damped forced vibration system, the peak steady-state amplitude occurs at what frequency ratio?

Answer: r = √(1 − 2ζ²)

The resonant peak in displacement occurs at r = √(1 − 2ζ²), which is slightly below 1 for underdamped systems.

A vibration isolator transmits 10% of the applied force to its foundation. What is its transmissibility ratio?

Answer: 0.10

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

A two-degree-of-freedom spring-mass system has how many natural frequencies?

Answer: 2

An n-DOF system always has exactly n natural frequencies (and mode shapes).

For vibration isolation to be effective (TR < 1) in an undamped system, the frequency ratio r = ω/ω_n must satisfy:

Answer: r > √2

For an undamped isolator, TR = 1/|1 − r²| √2 ≈ 1.414.