📚 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–3 | Page–2
Energy Graphs in Simple Harmonic Motion
Graphs are the fastest weapons in JEE Advanced
Why Energy Graphs are Crucial
- Most JEE Advanced questions are visual
- Graphs avoid long calculations
- Help instantly identify traps
1. Energy vs Displacement (x)
Potential Energy:
U = ½ kx²
- Parabolic curve opening upward
- Minimum at x = 0
- Maximum at x = ±A
Kinetic Energy:
K = ½ mω²(A² − x²)
- Inverted parabola
- Maximum at x = 0
- Zero at x = ±A
Total Energy:
E = constant (horizontal straight line)
Important Intersection Point
- K = U when x = ± A / √2
- Both equal to E / 2
⚠ IIT Favorite Point
2. Energy vs Time (t)
Assume displacement:
x = A sin(ωt)
Potential Energy vs Time:
U = ½ kA² sin²(ωt)
- Always positive
- Period = T/2
Kinetic Energy vs Time:
K = ½ kA² cos²(ωt)
- Maximum when U is minimum
- Period = T/2
IIT Trap – Period Confusion
- Displacement period = T
- Energy period = T/2
Energy repeats twice in one oscillation
Phase Relationship
| Quantity | Phase Relation |
| Displacement & Velocity | 90° |
| Kinetic & Potential Energy | 90° |
| Energy & Displacement | Dependent on square |
Area Under Energy–Time Graph
- Represents energy × time
- No physical work meaning
- Used only for comparison
JEE Advanced Question Patterns
- Identify correct graph
- Compare energy at two times
- Energy ratio from graph
- Phase-based reasoning
Topper Strategy
Never calculate energy graph values point-by-point.
Recognize shape → answer instantly.
Next in Stage–3
- Page–3: Turning Points & Energy Barriers
- Page–4: PYQs on Energy Graphs
Stage–3 | Page–2 Completed ✔ Graph mastery unlocked 📈
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