Free Simple Harmonic Motion MCQs with Answers
466 Simple Harmonic Motion MCQs from Physics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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466 questions · page 7 of 24
- A. 0.27 J
- B. 0.54 J
- C. 0.81 J
- D. 1.08 J
Explanation: E = mgh = mgL (1 - Cos θ ) = 0.2 x 9.8 x 1.6 = 0.27 J.
Correct answer: 0.27 J- A. 0.3π m/s
- B. 0.6π m/s
- C. 0.9π m/s
- D. 1.2 m/s
Explanation: ω = 2π/T = 5π rad/s.vmax = Aω = 0.06 × 5π = 0.3π m/s.
Correct answer: 0.3π m/s- A. 10 rad/s
- B. 14.14 rad/s
- C. 20 rad/s
- D. 28.28 rad/s
Explanation: keq = k1 + k2 = 400 N/m.ω = √keq /m = √400/2 = 14.14 rad/s.
Correct answer: 14.14 rad/s- A. 1.52 S
- B. 1.75 s
- C. 2.00 s
- D. 2.25 s
Explanation: Effective geff = g + a = 11.8 m/s².Period T = 2π √L/geff ≈ 1.52s.
Correct answer: 1.52 S- A. 0.025 Hz
- B. 0.050 Hz
- C. 0.075 Hz
- D. 0.100 Hz
Explanation: Beat frequency fbeat = |f1 - f2|.With f = 1/2π and weak coupling,fbeat ≈ K/4πmfo ≈ 0.025 Hz.
Correct answer: 0.025 Hz- A. 36.8%
- B. 63.2%
- C. 13.5%
- D. 86.5%
Explanation: Energy decays as E = E₀ e(-b/m*t).For one cycle (T = 2π / ω), the fraction remaining is e-b/m*t ≈ e-2π*b/mω0 ≈ 0.368 or 36.8%.
Correct answer: 36.8%- A. g + a
- B. √g² + a²
- C. g - a
- D. √g² - a²
Explanation: In the non-inertial frame of the train, a fictitious force -ma acts horizontally.
Correct answer: √g² + a²- A. Maximum displacement from the mean position
- B. Centre position
- C. Half of the maximum displacement from mean position
- D. Mean position
Explanation: A simple harmonic motion (SHM), acceleration is maximum when the object is at its maximum displacement from the mean position.
Correct answer: Maximum displacement from the mean position- A. 2 rad/s
- B. 5 rad/s
- C. 10 rad/s
- D. 20 rad/s
Explanation: K = ½ mω²A2 . Substituting; 0.4 = ½ (0.25)ω² (0.08)2 .Solving; ω = √0.4 x 2 / 0.25×0.0064 = 5 rad/s.
Correct answer: 5 rad/s- A. 5 rad/s
- B. 10 rad/s
- C. 14.14 rad/s
- D. 20 rad/s
Explanation: The equivalent spring constant for parallel springs is keq = k1 + k2 = 100 +300 = 400 N/m.
Correct answer: 14.14 rad/s131. A spring of spring constant k is cut into two equal parts. What is the spring constant of each part?
- A. k/2
- B. k
- C. 2k
- D. 4k
Explanation: The spring constant k is inversely proportional to the length. Cutting the spring in half doubles the spring constant, so each part has…
Correct answer: 2k- A. 0.54 m/s
- B. 0.72 m/s²
- C. 1.08 m/s²
- D. 1.44 m/s2
Explanation: The maximum acceleration amax = Aω² = 0.03 × 62 = 1.08 m/s².
Correct answer: 1.08 m/s²- A. 0.0785s
- B. 0.1 s
- C. 0.157s
- D. 0.2 s
Explanation: The angular frequency ω = √k/m = √320/0.8 = 20rad/s. The time to reach equilibrium from maximum displacement is ;t = T/4 = π/2ω = π/2 x 20…
Correct answer: 0.0785s- A. 1.0
- B. 1.5
- C. 2.0
- D. 3.0
Explanation: The amplitude ratio is given by Aresonance / A(fd) = fo / |fd-fo| , 2/ |3-2| = 2.
Correct answer: 2.0- A. 3.0 rad/s
- B. 4.47 rad/s
- C. 5.0 rad/s
- D. 6.0 rad/s
Explanation: Using v = ωV √A2 - x² , we get 0.6 = ω√(0.15)2 - (0.05)2.Solving, ω = 0.6/√0.02 ≈ 4.47 rad/s.
Correct answer: 4.47 rad/s- A. 0.4 s
- B. 0.562 s
- C. 0.8 s
- D. 1.0 s
Explanation: The equivalent spring constant for series springs is keq = k/2 = 150/2 = 75 N/m. The period T = 2π √m/ keq = 2π √0.6/75 ≈ 0.562 s.
Correct answer: 0.562 s- A. 1.0 m/s
- B. 1.5 m/s
- C. 1.73 m/s
- D. 2.0 m/s
Explanation: Using energy conservation, v = ω √A2 - x2 = √k/m √A2 - (A/2)2 = √100/0.25 √0.1 which equals 1.73 m/s.
Correct answer: 1.73 m/s- A. 9.8 m/s²
- B. 12.0 m/s²
- C. 14.05 m/s²
- D. 16.0 m/s2
Explanation: Using T = 2π √L/g , we get g = 4π2L / T2 = 4π2 (0.8) / (1.5)2 ≈ 14.05 m/s2 .
Correct answer: 14.05 m/s²- A. 12 m/s²
- B. 18 m/s²
- C. 24 m/s2
- D. 30 m/s²
Explanation: The maximum acceleration amax = ω²A = k/m A = 160/0.4(0.06) = 24 m/s2 .
Correct answer: 24 m/s2- A. 0.25 s
- B. 0.5 s
- C. 1 s
- D. 2 s
Explanation: The angular frequency ω = 4π. The period T= 2π/ω = 2π/4π = 0.5s.
Correct answer: 0.5 s