📚 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 7
Simple Harmonic Motion (SHM) – Springs, Elastic Strings & Hybrid Systems

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1. Springs in Series (IIT Favorite)

When two or more springs are connected in series:

1 / k_eq = 1 / k₁ + 1 / k₂ + ...

Time period:

T = 2π √(m / k_eq)

Series connection increases time period

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2. Springs in Parallel

For springs attached side by side:

k_eq = k₁ + k₂ + ...

Time period:

T = 2π √(m / k_eq)

Parallel connection decreases time period

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3. Mixed Spring Systems (Advanced)

In complex networks:

• Reduce step-by-step
• Never assume symmetry blindly

Always find equivalent spring constant first

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4. Elastic String – Important Difference

Elastic string:

• No force when slack
• Force only when stretched

Tension = kx (only if stretched)

Motion may NOT be SHM for entire cycle

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5. SHM with Elastic String (Vertical Motion)

If equilibrium lies in stretched region:

• Motion about equilibrium is SHM

ω = √(k / m)

Key: equilibrium must be in stretched part

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6. Variable Mass Systems (Conceptual)

In most IIT problems:

• Mass change is slow
• SHM approximation still valid

Variable mass rarely changes ω directly

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7. SHM with Two Masses & One Spring

System:

• Two masses connected by a spring
• Both are free

Effective mass:

μ = (m₁ m₂) / (m₁ + m₂)

Angular frequency:

ω = √(k / μ)

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8. SHM of Pulley–Spring Hybrid

Key ideas:

• Use constraint equations
• Convert multiple motions into one variable

Constraint reduces degrees of freedom

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9. Common IIT Advanced Traps

• Assuming elastic string always active
• Ignoring spring mass (when specified)
• Wrong equivalent spring calculation

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Stage 3 – Page 7 Key Takeaways

✔ Equivalent spring constant controls SHM
✔ Elastic string ≠ spring
✔ Hybrid systems require constraint thinking

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— Stage 3 | Advanced SHM Systems —