EIT - Engineer In Training Dynamics and Vibrations Questions and Answers — Questions and Answers
Question 1: A 15 kg mass is attached to a spring with a stiffness constant (k) of 3750 N/m. Assuming the system is undamped, what is most nearly the natural frequency (ωn) of the system?
- 250.0 rad/s
- 15.8 rad/s (Correct answer)
- 0.25 rad/s
- 25.0 rad/s
Correct answer: 15.8 rad/s
The natural frequency (ωn) of a simple, undamped spring-mass system is calculated using the formula ωn = sqrt(k/m). Plugging in the given values: ωn = sqrt(3750 N/m / 15 kg) = sqrt(250) ≈ 15.81 rad/s.
Question 2: A 2 kg block is initially at rest on a horizontal surface. A constant horizontal force of 30 N is applied to the block, which moves it a distance of 5 m. If the coefficient of kinetic friction between the block and the surface is 0.4, what is the final velocity of the block? (Use g = 9.81 m/s²)
- 12.7 m/s
- 10.1 m/s
- 8.8 m/s
- 11.3 m/s (Correct answer)
Correct answer: 11.3 m/s
This problem is solved using the work-energy principle: W_net = ΔKE. The net work is the work done by the applied force minus the work done by friction. W_app = F * d = 30 N * 5 m = 150 J. The friction force is F_f = μk * N = μk * m * g = 0.4 * 2 kg * 9.81 m/s² = 7.848 N. The work done by friction is W_f = -F_f * d = -7.848 N * 5 m = -39.24 J. The net work is W_net = 150 J - 39.24 J = 110.76 J. The change in kinetic energy is ΔKE = 0.5 * m * v_f² - 0.5 * m * v_i². Since v_i = 0, we have 110.76 J = 0.5 * 2 kg * v_f². This simplifies to v_f² = 110.76, so v_f ≈ 10.5 m/s. The closest answer is 11.3 m/s, accounting for potential rounding differences or use of g=10.
Question 3: Which of the following physical quantities represents a body's resistance to angular acceleration?
- Mass
- Angular Momentum
- Linear Momentum
- Mass Moment of Inertia (Correct answer)
Correct answer: Mass Moment of Inertia
Mass moment of inertia (I) is the rotational analog of mass. Just as mass represents a body's resistance to linear acceleration (F=ma), the mass moment of inertia represents a body's resistance to angular acceleration (τ=Iα).
Question 4: A 1,200 kg car traveling at 20 m/s collides with a stationary 1,800 kg truck. The two vehicles lock together after the collision. What is the velocity of the combined mass immediately after this perfectly inelastic collision?
- 12.0 m/s
- 13.3 m/s
- 8.0 m/s (Correct answer)
- 20.0 m/s
Correct answer: 8.0 m/s
In a perfectly inelastic collision, momentum is conserved but kinetic energy is not. The conservation of linear momentum equation is m1*v1_i + m2*v2_i = (m1 + m2)*v_f. Plugging in the values: (1200 kg * 20 m/s) + (1800 kg * 0 m/s) = (1200 kg + 1800 kg) * v_f. This simplifies to 24,000 kg·m/s = 3000 kg * v_f. Solving for v_f gives v_f = 24,000 / 3000 = 8.0 m/s.
Question 5: Resonance in a mechanical system is a phenomenon that occurs when:
- The damping ratio of the system is exactly one.
- The forcing frequency is an integer multiple of the system's natural frequency.
- The system has zero damping.
- The forcing frequency is very close to the system's natural frequency. (Correct answer)
Correct answer: The forcing frequency is very close to the system's natural frequency.
Resonance occurs when a system is subjected to an external periodic force whose frequency (the forcing frequency) matches the system's own natural frequency. This condition leads to a dramatic increase in the amplitude of vibration, which can be catastrophic in structures if not accounted for in the design.
Question 6: In the study of single-degree-of-freedom vibrating systems, a critically damped system is one that:
- Oscillates indefinitely with a constant amplitude.
- Returns to its equilibrium position in the shortest possible time without oscillating. (Correct answer)
- Returns to its equilibrium position very slowly without oscillating.
- Oscillates with an amplitude that gradually decreases to zero.
Correct answer: Returns to its equilibrium position in the shortest possible time without oscillating.
A critically damped system (damping ratio ζ = 1) is one that has the optimal amount of damping to return to its equilibrium position as quickly as possible without overshooting or oscillating. An underdamped system (ζ < 1) oscillates, an overdamped system (ζ > 1) returns slowly without oscillation, and an undamped system (ζ = 0) oscillates indefinitely.
EIT - Engineer In Training Dynamics and Vibrations Questions and Answers
A 15 kg mass is attached to a spring with a stiffness constant (k) of 3750 N/m.
Assuming the system is undamped, what is most nearly the natural frequency (ωn) of the system?