Simple Harmonic Motion (SHM)

15 Golden Rules with Examples (JEE Advanced Level)

RULE 1️⃣: Identify the TYPE before solving

First decide: Time-based, Energy-based, or Graph-based.

Example: “Time taken to move from x₁ to x₂” → Phase angle method.

RULE 2️⃣: Never calculate time directly from velocity

Time questions must be solved using phase (θ), not equations.

Example: Convert x = A/2 → θ = π/6 → t = T/12.

RULE 3️⃣: Energy beats equations

If position and speed are involved, use energy conservation.

Example: Same speed at +x and −x → Energy symmetry.

RULE 4️⃣: Mean vs Extreme decides everything

Velocity max at mean, acceleration max at extreme.

Example: Question asks “maximum acceleration” → look at extreme.

RULE 5️⃣: Direction matters more than magnitude

Always check sign of acceleration and velocity.

Example: Displacement negative → acceleration positive.

RULE 6️⃣: Graph slope = hidden answer

Slope tells velocity or acceleration.

Example: a–x graph slope = −ω².

RULE 7️⃣: Amplitude does NOT affect time period

Never mix amplitude with time period.

Example: Doubling amplitude → T unchanged.

RULE 8️⃣: Same speed ≠ same position

Same speed occurs at symmetric positions.

Example: Speed same at +x and −x due to energy.

RULE 9️⃣: Phase difference solves 50% time questions

Phase change directly gives time.

Example: Δθ = π/3 → t = T/6.

RULE 🔟: Never panic on long questions

Length ≠ difficulty. JEE hides shortcuts.

Example: Long calculation → symmetry or elimination exists.

RULE 1️⃣1️⃣: Restoring force decides SHM

If force ∝ displacement and opposite → SHM.

Example: Non-linear force → NOT SHM.

RULE 1️⃣2️⃣: Kinetic & potential energy crossover is fixed

KE = PE at x = A/√2.

Example: Energy equality question → direct result.

RULE 1️⃣3️⃣: Skip smartly

If stuck beyond 60 seconds → skip and return.

Example: Tough numerical early in exam → avoid ego trap.

RULE 1️⃣4️⃣: Analyze mistakes immediately

Wrong logic repeats if not fixed.

Example: Write “why I chose wrong option”.

RULE 1️⃣5️⃣: SHM is about THINKING, not formulas

Formulas are tools, thinking wins ranks.

Example: Topper solves in 3 lines, not 3 pages.

FINAL TOPPER MESSAGE

If you follow these 15 rules:

SHM fear disappears
Time per question drops sharply
Accuracy improves
Advanced questions feel logical

15 Golden Rules – Completed Successfully ✅

📚 IIT–JEE Physics Complete Library

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🔹 Simple Harmonic Motion (SHM) — Core Series

Coverage: Concepts → PYQs → Advanced Thinking → Exam Readiness

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

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