BME Dynamics and Vibrations 1 — Questions and Answers
Question 1: The natural frequency of a simple spring-mass system is given by:
- ωn = k/m
- ωn = √(k/m) (Correct answer)
- ωn = √(m/k)
- ωn = km
Correct answer: ωn = √(k/m)
The natural frequency of a single degree-of-freedom spring-mass system is ωn = √(k/m) radians per second.
Question 2: Resonance in a vibrating system occurs when:
- Damping equals stiffness
- Excitation frequency equals natural frequency (Correct answer)
- Amplitude equals zero
- Phase angle is zero
Correct answer: Excitation frequency equals natural frequency
Resonance occurs when the forcing frequency matches the system's natural frequency, causing theoretically infinite amplitude in undamped systems.
Question 3: The damping ratio ζ = 1 corresponds to which type of damping?
- Underdamped
- Overdamped
- Critically damped (Correct answer)
- Undamped
Correct answer: Critically damped
Critical damping (ζ = 1) produces the fastest return to equilibrium without oscillation, defining the boundary between underdamped and overdamped behavior.
Question 4: In Newton's second law for rotation, the torque is equal to:
- Iα (moment of inertia × angular acceleration) (Correct answer)
- mα
- Iω
- mv²
Correct answer: Iα (moment of inertia × angular acceleration)
The rotational form of Newton's second law is ΣT = Iα, where I is the mass moment of inertia and α is angular acceleration.
Question 5: The coefficient of restitution (e) for a perfectly plastic collision equals:
- 1
- 0.5
- 0 (Correct answer)
- Infinity
Correct answer: 0
In a perfectly plastic (inelastic) collision, the objects stick together and e = 0, meaning there is no rebound and maximum kinetic energy is lost.
Question 6: D'Alembert's principle transforms a dynamic problem into an equivalent:
- Thermal equilibrium problem
- Static equilibrium problem (Correct answer)
- Fluid flow problem
- Energy balance problem
Correct answer: Static equilibrium problem
D'Alembert's principle introduces an inertia force (-ma) to convert the dynamic equation F = ma into a static equilibrium form ΣF = 0.
BME Dynamics and Vibrations 1
The natural frequency of a simple spring-mass system is given by: