Simple Harmonic Motion (SHM)

100 Objective Questions with Answers (JEE Main + Advanced Level)

SECTION A: Core Concepts (Q1–20)

  1. Total energy in SHM depends on → Amplitude
  2. Velocity is maximum at → Mean position
  3. Acceleration is maximum at → Extreme position
  4. Time period depends on → m and k
  5. Phase difference between displacement & velocity → π/2
  6. Phase difference between velocity & acceleration → π/2
  7. At mean position, PE = → 0
  8. At extreme position, KE = → 0
  9. Graph of a vs x → Straight line
  10. Graph of PE vs x → Parabola
  11. Angular frequency ω = → √(k/m)
  12. Time period T = → 2π√(m/k)
  13. Maximum speed vmax = → ωA
  14. Maximum acceleration amax = → ω²A
  15. Mean position is → Equilibrium position
  16. Restoring force ∝ → Displacement
  17. SHM is projection of → Uniform circular motion
  18. Energy is conserved if → No damping
  19. Power at mean position → Zero
  20. Jerk is maximum at → Mean position

SECTION B: Time, Phase & Motion (Q21–40)

  1. Time from mean to extreme → T/4
  2. Time from A/2 to A → > T/8
  3. Motion fastest near → Mean position
  4. Motion slowest near → Extreme position
  5. Phase constant depends on → Initial condition
  6. Displacement zero but velocity non-zero at → Mean position
  7. Acceleration zero at → Mean position
  8. Displacement maximum at → Extreme position
  9. Velocity changes sign at → Mean position
  10. Acceleration changes sign at → Mean position
  11. Phase difference π gives → Opposite motion
  12. Time for half oscillation → T/2
  13. Time for full oscillation → T
  14. Displacement ∝ → sin(ωt)
  15. Velocity ∝ → cos(ωt)
  16. Acceleration ∝ → −sin(ωt)
  17. Energy oscillates with frequency → 2ω
  18. Velocity oscillates with frequency → ω
  19. Acceleration oscillates with frequency → ω
  20. PE + KE = → Constant

SECTION C: Energy & Graphs (Q41–60)

  1. PE = KE at x = → A/√2
  2. KE maximum when x = → 0
  3. PE maximum when x = → ±A
  4. Total energy graph vs time → Horizontal line
  5. Velocity vs x graph → Semi-circle
  6. Energy depends on → A²
  7. Doubling A makes energy → 4 times
  8. Doubling A makes time period → Same
  9. Energy proportional to → kA²
  10. Acceleration proportional to → x
  11. Force proportional to → x
  12. Work done in one cycle → Zero
  13. Power averaged over one cycle → Zero
  14. Mean speed over one cycle → 4A/T
  15. Mean velocity over one cycle → 0
  16. SHM graph symmetric about → Mean position
  17. Velocity is zero at → Extreme
  18. PE is zero at → Mean
  19. KE equals total energy at → Mean
  20. Acceleration direction → Towards mean

SECTION D: Springs, Gravity & Systems (Q61–80)

  1. Vertical spring SHM time period → Unaffected by g
  2. Inclined spring SHM time period → Same
  3. Parallel springs equivalent k → k₁ + k₂
  4. Series springs equivalent k → (k₁k₂)/(k₁+k₂)
  5. Doubling mass makes T → √2 times
  6. Doubling k makes T → 1/√2 times
  7. Gravity affects → Equilibrium position
  8. Damping reduces → Amplitude
  9. Damped SHM frequency → Almost same
  10. Critically damped system → No oscillation
  11. Overdamped system → Slow return
  12. Underdamped system → Oscillatory
  13. Mass sticks at mean → T increases
  14. Spring cut at mean → Uniform motion
  15. Energy decreases in damping → Exponentially
  16. Angular SHM variable → θ
  17. Angular SHM inertia → I
  18. Restoring torque ∝ → θ
  19. Angular frequency ∝ → √(k/I)
  20. Small oscillations valid when → θ small

SECTION E: Examiner Traps (Q81–100)

  1. Energy conserved always? → No
  2. Velocity zero at mean? → No
  3. Acceleration zero at extreme? → No
  4. Time equal for equal distance? → No
  5. Amplitude affects T? → No
  6. Power max at mean? → No
  7. Phase = displacement? → No
  8. SHM always sinusoidal? → Only ideal
  9. Damping changes T a lot? → No
  10. Velocity always sinusoidal? → Yes
  11. Acceleration linear with x? → Yes
  12. Energy linear with x? → No
  13. Graph a vs t sinusoidal? → Yes
  14. Velocity maximum at extreme? → No
  15. KE max at extreme? → No
  16. PE max at mean? → No
  17. SHM requires restoring force? → Yes
  18. Projection of UCM gives SHM? → Yes
  19. Mean velocity over cycle ≠ 0? → False
  20. SHM questions easy but tricky? → Yes

100 SHM Objective Questions Completed ✅
You are now EXAM-READY for SHM.

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🔹 Simple Harmonic Motion (SHM) — Core Series

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🔹 Simple Harmonic Motion (SHM) — Extended Series (30–56)

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