📚 IIT–JEE Physics Complete Learning Hub

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🔹 Core Physics Libraries

• 🔁 Simple Harmonic Motion (SHM) – Complete Library (IIT–JEE Advanced)
• 🌊 Mechanical Waves – JEE Advanced Objective Library
• 🧠 IIT–JEE Physics Complete Master Library

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🔹 Central Learning Platforms

• 🌐 Shaktimatha Learning Resource Hub
• 💬 Join Our WhatsApp Physics Learning Channel

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📌 Structured • Exam-Oriented • IIT–JEE Advanced Focused Learning

Stage–2 | Page–4
Graphs, Force & Phase Relations in SHM

Where most students lose marks — and toppers gain confidence

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Restoring Force in SHM

The defining condition of SHM:

F = −kx

• Force always points toward mean position
• Magnitude increases with displacement

IIT Key Insight:
Negative sign shows direction, not negativity of force.

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Acceleration in SHM

a = −ω²x

• Acceleration ∝ displacement
• Acceleration is maximum at extreme
• Acceleration is zero at mean

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Phase Relationship (Must Memorize)

Quantity	Phase Relation
Displacement (x)	sin(ωt + φ)
Velocity (v)	cos(ωt + φ) → leads x by π/2
Acceleration (a)	−sin(ωt + φ) → opposite phase to x

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SHM Graphs – Conceptual Understanding

Graphs are frequently tested indirectly in IIT/JEE.

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1️⃣ Displacement–Time (x–t) Graph

• Pure sine or cosine wave
• Slope gives velocity
• Curvature gives acceleration

At mean position: slope maximum
At extreme: slope zero

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2️⃣ Velocity–Time (v–t) Graph

• Cosine or sine curve
• Phase shifted by π/2 from x–t
• Area under curve ≠ displacement (non-uniform)

Velocity is maximum at mean position

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3️⃣ Acceleration–Time (a–t) Graph

• Opposite phase to displacement
• Maximum at extreme positions
• Zero at mean position

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One Look Comparison (JEE Favorite)

Position	x	v	a
Mean	0	Max	0
Extreme	Max	0	Max

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Energy Graphs in SHM

• Kinetic Energy ∝ cos²(ωt + φ)
• Potential Energy ∝ sin²(ωt + φ)
• Total Energy = constant

KE + PE = Constant

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IIT Traps Using Graphs

• Confusing slope with value
• Assuming area gives displacement always
• Ignoring phase difference

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How IIT Toppers Use Graphs

• Convert graph → equation mentally
• Identify phase instantly
• Check velocity sign before answering

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Next: Stage–2 Page–5

• Energy method in SHM
• KE–PE conversion tricks
• JEE Advanced numerical traps

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Stage–2 Page–4 Completed ✔ You can now read any SHM graph confidently 📈