📚 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–2
Energy Method in Simple Harmonic Motion
When force approach becomes messy, energy saves you
Why IIT Loves Energy Method
- No direction confusion
- No sign mistakes
- Works even when force is complex
IIT Tip:
If you see turning points, maximum speed, or amplitude → think energy.
If you see turning points, maximum speed, or amplitude → think energy.
Total Mechanical Energy in SHM
In ideal SHM (no friction):
Total Energy (E) = Constant
Energy has two parts:
- Kinetic Energy (KE)
- Potential Energy (PE)
Potential Energy in SHM
Restoring force:
F = −kx
Potential energy function:
PE = ½ kx²
Important: Zero PE is taken at equilibrium.
Kinetic Energy in SHM
KE = ½ mv²
Velocity is maximum at equilibrium, zero at extreme positions.
Total Energy Expression
At extreme position (x = A):
E = ½ kA²
This is the total energy of SHM.
Energy Distribution at Any Position x
KE = ½ k (A² − x²)
PE = ½ k x²
Sum remains constant.
Velocity–Position Relation (Very Important)
v = ω √(A² − x²)
This formula is frequently used in JEE Advanced.
Special Energy Cases (Must Remember)
| Position | KE | PE |
|---|---|---|
| Equilibrium (x = 0) | Maximum | Zero |
| Extreme (x = ±A) | Zero | Maximum |
| x = A/√2 | = PE | = KE |
IIT Traps Using Energy
- Energy is scalar – direction not needed
- Do not confuse displacement with distance
- Amplitude may change if energy changes
Self-Check (IIT Mindset)
- Can I find speed without time?
- Can I find position without phase?
- Can I locate turning points?
What Comes in Stage–2 Page–3?
- Phase, phase constant & phase difference
- Time-based analysis
- Multiple SHM comparison
Stage–2 Page–2 Completed ✔ You are now dangerous to tough SHM problems 😄
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