📚 IIT–JEE Physics Complete Learning Hub
🔹 Core Physics Libraries
- 🔁 Simple Harmonic Motion (SHM) – Complete Library (IIT–JEE Advanced)
- 🌊 Mechanical Waves – JEE Advanced Objective Library
- 🧠 IIT–JEE Physics Complete Master Library
🔹 Central Learning Platforms
📌 Structured • Exam-Oriented • IIT–JEE Advanced Focused Learning
Stage–2 | Page–8
Velocity–Displacement Relation & Energy Method in SHM
Most scoring + most confusing part for students
Velocity–Displacement Relation
v² = ω² (A² − x²)
This equation connects position and velocity without time.
- Used heavily in JEE Advanced
- Works only for SHM
Special Positions – Must Remember
| Position | Velocity | Acceleration |
|---|---|---|
| x = 0 (Mean) | Maximum | 0 |
| x = ±A (Extreme) | 0 | Maximum |
| x = A/2 | ω√(3A²/4) | −ω²(A/2) |
Sign of Velocity
From v² equation, magnitude comes — sign must be decided separately.
Rule:
Check direction of motion from including diagram or phase
Check direction of motion from including diagram or phase
Energy Method in SHM
Total mechanical energy remains constant.
Total Energy = ½ kA² = ½ mω²A²
Potential Energy (PE)
PE = ½ kx² = ½ mω²x²
- Minimum at mean position
- Maximum at extreme position
Kinetic Energy (KE)
KE = ½ mω² (A² − x²)
- Maximum at mean position
- Zero at extremes
Energy Ratio at Position x
PE : KE = x² : (A² − x²)
Frequently used in numerical + MCQs.
IIT Trap #2 – Energy ≠ Velocity Graph
Students confuse:
- Energy vs displacement → parabola
- Velocity vs displacement → ellipse
Never mix graph interpretations
Topper Shortcut
- If energy asked → use energy equations
- If time asked → use equation of motion
- If position–velocity relation → use v² = ω²(A² − x²)
Typical JEE Advanced Questions
- Find velocity at given displacement
- Find displacement when KE = PE
- Fraction of total energy as KE
- Energy change between two positions
Next: Stage–2 Page–9
- Time period from energy method
- Mean speed vs average speed
- Advanced traps & mixed concepts
Stage–2 Page–8 Completed ✔ You now master SHM without time variable 🔥
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