Simple Harmonic Motion (SHM)

Final Capsule – 1 Page Exam-Day Checklist (JEE Advanced)

1️⃣ CORE CONDITIONS (DON’T FORGET)

Restoring force ∝ displacement and opposite in direction
Acceleration decides SHM, not velocity
If force is non-linear → NOT SHM

2️⃣ MEAN vs EXTREME (MOST COMMON CONFUSION)

Position	Velocity	Acceleration	Energy
Mean	Maximum	Zero	KE max
Extreme	Zero	Maximum	PE max

3️⃣ MUST-REMEMBER FORMULAS

x = A sin(ωt + φ) or A cos(ωt + φ)
v = ω√(A² − x²)
a = −ω²x
v_max = Aω
a_max = ω²A

4️⃣ ENERGY SHORTCUTS (RANK BOOSTER)

Total energy = ½mω²A² (constant)
KE = ½mω²(A² − x²)
PE = ½mω²x²
KE = PE at x = A / √2
Same speed at +x and −x

5️⃣ TIME & PHASE (MOST IMPORTANT)

θ = ωt
Δt = Δθ / ω
Use phase for ALL time questions
Never calculate time using velocity equation

6️⃣ GRAPH QUICK CHECK

x–t → sine curve
v–t → cosine curve
a–x → straight line (slope = −ω²)
KE–x → parabola

7️⃣ JEE ADVANCED TRAPS (AVOID THESE)

Assuming rolling or equilibrium without proof
Mixing kinematics with SHM equations
Ignoring sign of acceleration
Over-calculating when symmetry works
Panic on long questions

8️⃣ EXAM-HALL STRATEGY

Identify type: Time / Energy / Graph
Decide method before writing
If stuck after 60 seconds → skip
Return in second round

9️⃣ 30-SECOND MENTAL MANTRA

TIME → PHASE
SPEED → ENERGY
GRAPH → SLOPE
MEAN → v_max
EXTREME → a_max

SHM FINAL CAPSULE COMPLETED ✅
Read this once before exam → save 10–15 marks

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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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