📚 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 8
Simple Harmonic Motion – Damped Oscillations & Energy Decay
1. What is Damped SHM?
Damped SHM occurs when a resistive force opposes motion and is proportional to velocity.
Fdamping = − b v
- b → damping constant
- Energy gradually decreases
2. Equation of Motion (Important)
m d²x/dt² + b dx/dt + kx = 0
This is NOT simple SHM equation
3. Types of Damping (Must Memorize)
| Type | Condition | Nature |
|---|---|---|
| Underdamped | b² < 4mk | Oscillatory (most common) |
| Critical damping | b² = 4mk | Fastest return, no oscillation |
| Overdamped | b² > 4mk | No oscillation |
4. Underdamped Motion (JEE Favorite)
Displacement:
x = A e−(b/2m)t sin(ω′t + φ)
Where:
ω′ = √(ω₀² − (b/2m)²)
5. Energy Decay in Damped SHM
Total energy decreases exponentially:
E = E₀ e−(b/m)t
Amplitude decays slower than energy
6. Logarithmic Decrement (Advanced Concept)
Defined as:
λ = ln(A₁ / A₂)
Also:
λ = (b / 2m) T
Used to measure damping experimentally
7. Quality Factor (Q-Factor)
Defines sharpness of oscillation:
Q = ω₀ / (2β)
Where:
β = b / 2m
High Q → slow energy loss
8. Common IIT Traps
- Using ω instead of ω′
- Confusing amplitude decay with energy decay
- Assuming damping changes equilibrium position
Stage 3 – Page 8 Summary
✔ Damping force ∝ velocity
✔ Energy decays exponentially
✔ Logarithmic decrement is exam-oriented
— Stage 3 | Damped Oscillations —
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