Stage 3 – Page 10
Simple Harmonic Motion – Final Capsule (JEE Advanced)


1. One-Line SHM Definition (Exam Safe)

A motion is SHM if acceleration is directly proportional to displacement and always directed towards the mean position.

If restoring force ∝ displacement → SHM


2. Master Formula Sheet (Must-Recall)

Quantity Formula
Angular frequency ω = √(k/m)
Time period T = 2π/ω
Maximum speed vmax = Aω
Maximum acceleration amax = Aω²
Total energy E = ½kA²

3. Energy Distribution (High Frequency PYQ)

  • At mean position → KE maximum
  • At extreme position → PE maximum
  • Total energy constant (ideal SHM)

If energy changes → NOT ideal SHM


4. Spring + Gravity (Vertical SHM Trap)

Gravity shifts mean position only.

Time period independent of gravity

Most students wrongly include g in T


5. Circular Motion Link (Direct JEE Question)

Projection of uniform circular motion on diameter → SHM

x = A cos(ωt)

Phase interpretation is compulsory


6. Damping – Absolute Clarity

  • Light damping → oscillatory
  • Critical damping → fastest return, no oscillation
  • Heavy damping → slow return

Frequency decreases with damping


7. Resonance – Ultimate Trap Zone

Displacement resonance ≠ velocity resonance

  • Displacement resonance < ω₀
  • Velocity resonance = ω₀
  • Power resonance = ω₀

Never assume resonance blindly


8. PYQ Thinking Pattern

  • Identify restoring force direction
  • Check proportionality with displacement
  • Convert physical situation to equation
  • Eliminate non-SHM motions

9. 5 Golden Exam-Day Rules

  1. Never rush phase-based questions
  2. Always draw rough diagram
  3. Check limiting cases
  4. Dimensions must match
  5. Re-read resonance questions twice

FINAL SHM SUMMARY

✔ SHM = restoring force + proportionality
✔ Energy & phase are key
✔ Damping & resonance decide rank


🎯 STAGE 3 COMPLETE – SHM MASTERED 🎯

Next: Waves / Oscillations Mixed PYQs

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