📚 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–3
Phase, Phase Constant & Time Analysis in SHM

This page separates average students from IIT rankers

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General Equation of SHM

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

The term (ωt + φ) is called the phase.

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What is Phase?

Phase tells:

• Where the particle is
• Which direction it is moving
• How much energy it has

IIT Insight:
Two particles at same position may have different phases.

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Phase Constant (φ)

Phase constant depends on initial conditions:

• Initial position
• Initial direction of motion
• Initial velocity

At t = 0 → Phase = φ

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How to Find Phase Constant (Stepwise)

1. Write SHM equation
2. Substitute t = 0
3. Use given initial position
4. Check direction using velocity sign

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Velocity in SHM (Phase Based)

v = Aω cos(ωt + φ) (for sine form)

v = −Aω sin(ωt + φ) (for cosine form)

Sign of velocity decides direction.

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Important Phase Positions (JEE Favorite)

Phase	Position	Velocity
0	Extreme	Zero
π/2	Mean	Maximum
π	Opposite Extreme	Zero
3π/2	Mean	Maximum (opposite)

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Time Calculation Between Two Positions

Use phase difference:

Δt = Δθ / ω

Where Δθ = difference in phase angles.

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Common IIT Time Questions

• Time from mean to extreme
• Time between two arbitrary points
• Time when KE = PE

Golden Result:
Time from mean to extreme = T/4

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Time When KE = PE

Condition:

x = ± A / √2

Corresponding phase angles help find time.

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IIT Traps with Phase

• Same position ≠ same phase
• Ignoring velocity direction
• Using sine instead of cosine blindly

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Think Like an IIT Topper

• Convert position problem → phase problem
• Convert time problem → angle problem
• Always draw mental sine/cosine graph

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Next: Stage–2 Page–4

• Acceleration & force phase relation
• SHM graphs (x–t, v–t, a–t)
• Advanced conceptual traps

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Stage–2 Page–3 Completed ✔ Now you control time in SHM ⏱️