📚 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–7
Phase, Initial Conditions & Writing SHM Equation

The heart of SHM problems in JEE Advanced

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General Equation of SHM

x = A sin(ωt + φ)
or
x = A cos(ωt + φ)

• A → Amplitude
• ω → Angular frequency
• φ → Phase constant (initial phase)

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What is Phase?

Phase (ωt + φ) tells the **state of motion** at any instant.

• Position
• Direction of velocity
• Acceleration sign

Same phase ⇒ same state of motion

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Phase Constant (φ)

Phase constant depends only on initial conditions.

• Initial position
• Initial velocity

φ is decided at t = 0

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Using Initial Conditions

At t = 0:

x(0) = A sin φ
v(0) = Aω cos φ

• Two equations → solve for A and φ
• Sign of velocity is critical

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Choosing sin or cos Form

• If motion starts from mean position → use sin
• If motion starts from extreme position → use cos

Choice is for convenience — both are equivalent

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Standard Initial Conditions (Must Memorize)

• x = 0, v = +max → x = A sin ωt
• x = +A, v = 0 → x = A cos ωt
• x = −A, v = 0 → x = −A cos ωt
• x = 0, v = −max → x = −A sin ωt

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IIT Trap #1 – Wrong Quadrant of φ

Many students find tan φ but choose wrong quadrant.

Rule:
Always use sign of x(0) and v(0)

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Phase Difference Between Two Particles

ΔPhase = φ₂ − φ₁

• Same ω required
• Phase difference decides relative motion

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Phase Difference ↔ Time Lag

Δt = Δφ / ω

Frequently asked in match-the-following questions.

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How Toppers Write SHM Equation Fast

• Fix origin at equilibrium
• Decide sign of displacement
• Check velocity direction at t = 0
• Choose sin or cos smartly
• Write equation in one line

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Next: Stage–2 Page–8

• Velocity–displacement relations
• Energy method vs equation method
• High-level JEE applications

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Stage–2 Page–7 Completed ✔ You now control phase like an IIT topper 🔥