Oscillations & Simple Harmonic Motion (SHM)

Stage 1 – Page 10 | Damping, Forced Oscillations & Resonance

1. What Is Damping?

Damping is the gradual loss of energy of an oscillating system due to resistive forces like air friction, viscous force, or internal friction.

Because of damping, amplitude decreases with time.

2. Types of Damping

Light Damping – Oscillations continue with slowly decreasing amplitude
Critical Damping – System returns to equilibrium in minimum time without oscillation
Heavy (Over) Damping – Very slow return to equilibrium

Exam Insight:
Critical damping is fastest non-oscillatory motion.

3. Effect of Damping on Time Period

For light damping:

T_damped > T_natural

Time period slightly increases due to damping.

4. Forced Oscillations

When an external periodic force acts on a system, the system undergoes forced oscillations.

Frequency of oscillation = frequency of applied force.

5. Resonance

Resonance occurs when frequency of applied force = natural frequency.

At resonance:

Amplitude becomes maximum
Energy absorption is maximum

Important:
Resonance frequency ≠ natural frequency in damped systems.

6. Resonance Curve

Amplitude vs frequency graph is called resonance curve.

Sharp peak → low damping
Broad peak → high damping

7. Quality Factor (Q)

Quality factor measures sharpness of resonance:

Q = ω₀ / Δω

High Q → sharp resonance
Low Q → poor resonance

8. Real-Life Examples

Car shock absorbers → critical damping
Radio tuning → resonance
Bridge collapse → dangerous resonance
Seismograph → forced oscillations

9. IIT/JEE Common Traps

Confusing resonance frequency with natural frequency
Ignoring effect of damping
Wrong interpretation of resonance curve
Assuming amplitude grows indefinitely

10. Final Exam Takeaway

This page tests conceptual clarity more than formulas. Most questions are reasoning-based.

Master Idea:
Resonance is powerful but dangerous — control damping.

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