📚 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–10
SHM Graphs – x–t, v–t, a–t (JEE Advanced Level)

Most conceptual + multi-correct topic in SHM

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Fundamental SHM Equations

x = A sin(ωt + φ)
v = Aω cos(ωt + φ)
a = −ω²x

• All SHM graphs are phase-shifted versions of each other
• Amplitude and frequency are fixed

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Displacement–Time (x–t) Graph

• Pure sine or cosine wave
• Period = T
• Slope at any point = velocity

Key Points:
At mean position → slope maximum
At extreme position → slope zero

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IIT Trap #1 – Slope Confusion

• Slope ≠ speed (it is velocity)
• Sign of slope matters

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Velocity–Time (v–t) Graph

• Cosine graph if x is sine
• Phase difference of π/2 with x–t graph

Maximum velocity = Aω

Area under v–t graph = displacement

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IIT Trap #2 – Area Under Curve

• Positive area ≠ total distance
• Opposite signs cancel

Distance requires absolute area

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Acceleration–Time (a–t) Graph

• Also sinusoidal
• Always opposite in phase to x–t graph

a = −ω²x
When x is maximum → a is maximum (opposite sign)

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Phase Relationship Summary

Graph Pair	Phase Difference
x and v	π/2
v and a	π/2
x and a	π

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JEE Advanced Multi-Correct Logic

• Same x → same a
• Same |v| ≠ same position
• Same graph shape ≠ same phase

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Time Calculation from Graphs

• Use periodicity
• Use symmetry (half / quarter cycle)
• Avoid calculus unless forced

Graph problems reward visualization, not formulas

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Frequently Asked Advanced Questions

• Matching x–t with v–t graphs
• Finding acceleration from slope
• Area interpretation traps
• Counting zero crossings

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Topper Strategy

• Always mark mean & extreme positions
• Note direction of motion
• Use phase shift mentally

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What Comes Next?

• Stage–3: Energy Graphs in SHM
• Advanced PYQs with graphs
• Multi-body SHM systems

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Stage–2 Completed ✔ You have crossed the hardest conceptual zone 🚀