NCEES Dynamics 5 — Questions and Answers
Question 1: A 2 kg mass on a spring (k = 200 N/m) undergoes simple harmonic motion. What is its natural frequency ωn?
- 10 rad/s (Correct answer)
- 100 rad/s
- 5 rad/s
- √2 rad/s
Correct answer: 10 rad/s
ωn = √(k/m) = √(200/2) = √100 = 10 rad/s.
Question 2: A satellite in circular orbit at radius r from the Earth's center has speed v. If r doubles, what happens to v?
- v decreases by factor √2 (Correct answer)
- v doubles
- v halves
- v stays the same
Correct answer: v decreases by factor √2
v = √(GM/r); doubling r gives v' = v/√2, a decrease by factor √2.
Question 3: What is the velocity of the center of mass of a system of particles with masses m1=2 kg (v1=3 m/s) and m2=4 kg (v2=−1 m/s)?
- 1/3 m/s (Correct answer)
- 2 m/s
- 1 m/s
- −1 m/s
Correct answer: 1/3 m/s
v_cm = (m1v1 + m2v2)/(m1+m2) = (6−4)/6 = 2/6 = 1/3 m/s.
Question 4: D'Alembert's principle converts a dynamic problem into an equivalent static problem by introducing:
- An inertia force −ma opposing acceleration (Correct answer)
- A gravity force mg downward
- An impulse equal to change in momentum
- A reaction torque I·ω
Correct answer: An inertia force −ma opposing acceleration
D'Alembert's principle adds the inertia vector −ma to the free-body diagram, yielding a pseudo-static equilibrium.
Question 5: A gyroscope spinning at high speed has its spin axis horizontal. When a torque is applied vertically, the axis precesses. The precession rate Ω is given by:
- Ω = M/(I·ω) (Correct answer)
- Ω = I·ω/M
- Ω = M·ω/I
- Ω = I/(M·ω)
Correct answer: Ω = M/(I·ω)
Precession rate Ω = M/(I·ω), where M is the applied torque, I is moment of inertia, and ω is spin rate.
Question 6: A 3 kg block rests on a surface with μk = 0.2 and is pushed by a 20 N force. What is the acceleration? (g = 9.81 m/s²)
- 4.75 m/s² (Correct answer)
- 6.67 m/s²
- 0.35 m/s²
- 8.47 m/s²
Correct answer: 4.75 m/s²
F_friction = μk·mg = 0.2×3×9.81 = 5.886 N; a = (20−5.886)/3 ≈ 4.71 m/s² ≈ 4.75 m/s².
Question 7: For a critically damped single-degree-of-freedom system, the damping ratio ζ equals:
- 1 (Correct answer)
- 0
- Greater than 1
- 0.707
Correct answer: 1
Critical damping occurs exactly when ζ = 1, providing the fastest return to equilibrium without oscillation.
NCEES Dynamics 5
A 2 kg mass on a spring (k = 200 N/m) undergoes simple harmonic motion.
What is its natural frequency ωn?