Module 5 Quiz
Test Your Knowledge
10 questions covering free vibrations, forced vibrations, resonance, RLC circuits, and the mechanical-electrical analogy.
1
A 3-kg mass on a spring with k = 27 N/m. What is the natural frequency ω0?
Answer: ω0 = √(27/3) = √9 = 3 rad/s.
2
Classify: m = 1, c = 4, k = 4.
Answer: c² = 16 = 4mk = 16. Critically damped.
3
For x'' + 25x = F0cos(ωt), at what ω does pure resonance occur?
Answer: ω0 = 5. Pure resonance when ω = 5.
4
What is the form of the resonance particular solution for x'' + ω0²x = F0cos(ω0t)?
Answer: xp = [F0/(2mω0)] t sin(ω0t). The factor of t makes amplitude grow linearly.
5
If ω0 = 12 and ω = 11.5, what is the beat frequency?
Answer: Beat frequency = |12 - 11.5| = 0.5 rad/s.
6
In an RLC circuit, what plays the role of mass?
Answer: Inductance L. Both mass and inductance resist changes (inertia in motion vs. inertia in current flow).
7
Classify the RLC circuit: L = 1, R = 2, C = 1/5.
Answer: R² = 4. 4L/C = 4(1)(5) = 20. Since 4 < 20: underdamped.
8
What is the impedance formula for a series RLC circuit driven at frequency ω?
Answer: Z = √[R² + (ωL - 1/(ωC))²]. Minimum impedance (resonance) when ωL = 1/(ωC).
9
A spring-mass has m=0.5, c=2, k=8. What is the analogous RLC circuit?
Answer: L = 0.5 H, R = 2 Ω, 1/C = 8 so C = 0.125 F.
10
Why does damping prevent true resonance (unbounded growth)?
Answer: Damping dissipates energy at a rate proportional to velocity (or current). At some amplitude, energy input from the forcing equals energy dissipated, creating a bounded steady state.