📚 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–1
Energy in Simple Harmonic Motion (IIT–JEE Advanced)
This stage converts formulas into instant visualization
Core Idea of Energy in SHM
In SHM, energy is not destroyed or created — it only transforms between kinetic and potential forms.
Total Mechanical Energy = Constant
Types of Energy in SHM
- Kinetic Energy (K)
- Potential Energy (U)
- Total Energy (E)
Potential Energy in SHM
U = ½ kx²
- Minimum at mean position
- Maximum at extreme positions
- Always positive
Graph: Parabola opening upward
IIT Trap #1 – Zero Potential Confusion
- U = 0 only at mean position
- Extreme position ≠ zero energy
Kinetic Energy in SHM
K = ½ mω²(A² − x²)
- Maximum at mean position
- Zero at extreme positions
Graph: Inverted parabola
Total Energy of SHM
E = ½ kA² = constant
- Independent of time
- Independent of position
Energy Transformation During Motion
| Position | Kinetic Energy | Potential Energy |
| Mean Position | Maximum | Zero |
| Extreme Position | Zero | Maximum |
| Intermediate | Partial | Partial |
Fraction of Energy (Advanced Focus)
At displacement x:
K / E = 1 − (x² / A²)
U / E = x² / A²
U / E = x² / A²
IIT Trap #2 – Half Energy Myth
- K = U does NOT occur at x = A/2
- Occurs at x = A / √2
Finding Speed Using Energy
v = ω√(A² − x²)
- Fastest method in JEE
- Avoid time equations when possible
Typical JEE Advanced Questions
- Find position where K = nU
- Compare energies at two positions
- Energy ratios without time
- Graph matching questions
Topper Insight
If energy is involved, forget time.
Energy problems are geometry, not algebra.
Next Pages in Stage–3
- Page–2: Energy vs Time Graphs
- Page–3: Turning Points & Energy Barriers
- Page–4: Advanced PYQs on Energy
Stage–3 | Page–1 Completed ✔ Energy foundation is now unshakeable ⚡
No comments:
Post a Comment