📚 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 3 – Page 5
Simple Harmonic Motion (SHM) – Energy Method & Potential Curve

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1. Why Energy Method is Powerful

In SHM, total mechanical energy remains constant. Energy method avoids time and directly links position, velocity, and force.

Total Energy (E) = Kinetic Energy + Potential Energy

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2. Potential Energy in SHM

For a spring–mass SHM:

U = ½ kx²

• Minimum PE at mean position (x = 0)
• Maximum PE at extreme position (x = ±A)

SHM exists because PE curve is parabolic near equilibrium

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3. Kinetic Energy Expression

Since total energy is constant:

K = E − U = ½k(A² − x²)

Velocity at any position:

v = ω√(A² − x²)

Maximum velocity occurs at x = 0

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4. Total Energy of SHM

At extreme position:

E = ½kA² = ½mω²A²

• Depends only on amplitude
• Independent of mass distribution

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5. Energy Distribution Graph (Very Important)

• PE vs x → Parabola opening upward
• KE vs x → Inverted parabola
• Total Energy → Horizontal line

IIT often asks intersection logic of KE and PE curves

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6. Stability of Equilibrium (Advanced Thinking)

Equilibrium position is decided by potential energy curve.

• Stable: PE minimum
• Unstable: PE maximum
• Neutral: PE constant

Stable equilibrium ⇒ small oscillations possible

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7. Small Oscillations Concept (IIT Favorite)

Near equilibrium, any smooth potential curve can be approximated as:

U(x) ≈ U₀ + ½ k_eff x²

This leads to SHM with:

ω = √(k_eff / m)

This concept converts complex systems into SHM

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8. Turning Points via Energy

• At turning point: K = 0
• All energy stored as PE

Turning point is defined by energy, not force

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9. Typical IIT Traps

• Zero velocity ≠ zero force
• Maximum PE ≠ instability
• Amplitude decided by energy, not position

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Stage 3 – Page 5 Key Takeaways

✔ Energy method removes time dependency
✔ SHM exists near any stable equilibrium
✔ Potential curve decides motion nature

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— Stage 3 | SHM Energy Mastery —