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 8 of 24
- A. 100 N/m
- B. 150 N/m
- C. 200 N/m
- D. 250 N/m
Explanation: The spring constant k = F/x = 8 / 0.04 = 200 N/m.
Correct answer: 200 N/m- A. 5 rad/s
- B. 8 rad/s
- C. 10 rad/s
- D. 12 rad/s
Explanation: The maximum kinetic energy K = ½ mω²A². Substituting ; 0.096 = ½ (0.3)ω2 (0.08)2 . Solving gives ω = 10 rad/s.
Correct answer: 10 rad/s- A. 1.59 Hz
- B. 3.18 Hz
- C. 4.77 Hz
- D. 6.37 Hz
Explanation: The frequency f is given by f = 1/2π √k/m = 1/2π √80/0.2 ≈ 3.18 Hz.
Correct answer: 3.18 Hz- A. Angular acceleration
- B. Tangential acceleration
- C. Linear acceleration
- D. Radial acceleration
Explanation: Centripetal acceleration is the acceleration that keeps an object moving in a circular path; it points toward the center of the circle.
Correct answer: Radial acceleration- A. 3 rad/s
- B. 5 rad/s
- C. 6 rad/s
- D. 8 rad/s
Explanation: The maximum speed vmax in SHM is given by vmax = Aω. Thus, ω = vmax/A = 0.6 / 0.12 = 5 rad/s.
Correct answer: 5 rad/s146. A simple pendulum of length 1.6 m is on Earth (g = 9.8m/s²). What is its period of oscillation?
- A. 2.0 s
- B. 2.54 s
- C. 3.0 s
- D. 4.0 s
Explanation: The period T of a simple pendulum is given by T = 2π√L/g. Substituting the values, T = 2π√1.6/9.8 ≈ 2.54s.
Correct answer: 2.54 s- A. 10 rad/s
- B. 14.14 rad/s
- C. 20 rad/s
- D. 28.28 rad/s
Explanation: The angular frequency ω is given by ω = √k/m . Substituting the values, we get ω √200/0.5 = √400 = 20rad/s.
Correct answer: 20 rad/s- A. ωsym = √k/m , ωanti = √k+2K/m
- B. ωsym = √k+K/m , ωanti = √k/m
- C. ωsym = √2k+K/m , ωanti = √K/m
- D. ωsym = √k/m , ωanti = √2k + K/m
Explanation: In the symmetric mode both masses move together, so only the outer springs (k) affect the motion.
Correct answer: ωsym = √k/m , ωanti = √k+2K/m- A. 5 rad/s
- B. 10 rad/s
- C. 15 rad/s
- D. 20 rad/s
Explanation: Angular frequency ω = √(k / m) = √(50 / 0.5) = √100 = 10 rad/s.
Correct answer: 10 rad/s- A. 8.0 m/s²
- B. 9.87 m/s²
- C. 10.5 m/s²
- D. 12.0 m/s²
Explanation: Period T = 2π √(L / g). Rearrange: g = 4π² L / T² = 4 × π² × 1 / 2² ≈ 39.48 / 4 ≈ 9.87 m/s².
Correct answer: 9.87 m/s²- A. 0.5 m/s
- B. 0.71 m/s
- C. 1.0 m/s
- D. 1.41 m/s
Explanation: Maximum speed vmax = Aω = A √(k / m) = 0.1 × √(100 / 2) = 0.1 × √50 ≈ 0.1 × 7.07 ≈ 0.71 m/s.
Correct answer: 0.71 m/s- A. 0.1458 m
- B. 0.162 m
- C. 0.18 m
- D. 0.2 m
Explanation: Amplitude decreases by 10% per cycle, so A = A × (0.9) . After 2 cycles: A = 0.2 × (0.9)² = 0.2 × 0.81 = 0.162 m.
Correct answer: 0.162 m- A. 0.079 J
- B. 0.158 J
- C. 0.316 J
- D. 0.474 J
Explanation: Total energy E = ½ k A². Angular frequency ω = 2πf = 2π × 2 = 4π rad/s. k = mω² = 1 × (4π)² ≈ 157.91 N/m. E = ½ × 157.91 × (0.05)² ≈ 0.158 J
Correct answer: 0.158 J- A. 0.99 m/s
- B. 1.4 m/s
- C. 1.96 m/s
- D. 2.8 m/s
Explanation: Energy conservation: mgh = ½mv². Cancel m: v² = 2gh = 2 × 9.8 × 0.1 = 1.96, v = √1.96 ≈ 1.4 m/s.
Correct answer: 1.4 m/s- A. 0.05 m
- B. 0.1 m
- C. 0.15 m
- D. Infinity
Explanation: At resonance (driven at natural frequency), with no damping, the amplitude theoretically approaches infinity.
Correct answer: Infinity- A. 7.5 m/s²
- B. 9.0 m/s²
- C. 10.5 m/s²
- D. 12.3 m/s²
Explanation: For a simple pendulum g = 4π²L/T² = 4π²(0.8)/(1.6)² ≈ 12.3 m/s².
Correct answer: 12.3 m/s²- A. 0.1
- B. 0.2
- C. 0.3
- D. 0.4
Explanation: Damping ratio ζ = b / (2√(mk)) = 2 / (2 × √(0.5 × 50)) = 2 / (2 × √25) = 2 / 10 = 0.2.
Correct answer: 0.2- A. 0.1 m
- B. 0.141 m
- C. 0.173 m
- D. 0.2 m
Explanation: KE = PE when ½mv² = ½kx². Total energy E = ½kA². At x, PE = ½kx², KE = E - PE = ½kA² - ½kx².
Correct answer: 0.141 m- A. At crest and trough
- B. At mean position
- C. At all points equally
- D. At nodes only
Explanation: Velocity is maximum when displacement = 0.
Correct answer: At mean position- A. Half oscillation
- B. One oscillation
- C. Two oscillations
- D. One-fourth oscillation
Explanation: A complete oscillation is the motion of a particle from its mean position → extreme position → opposite extreme → back to mean position.
Correct answer: One oscillation