Physics Class 11 Oscillations – NCERT Quick Revision

Introduction

Oscillations are repetitive back-and-forth motions of a body about a mean position. Many natural phenomena such as the swinging of a pendulum, vibrations of a guitar string, or the motion of springs show oscillatory motion. In physics, the study of oscillations helps us understand waves, sound, alternating currents, and even atomic vibrations.

Key Concepts of Oscillations

1. Oscillatory Motion
   • A motion in which a particle moves to and fro about a fixed equilibrium position.
   • Example: Simple pendulum, mass attached to a spring.
2. Types of Oscillations
   • Free Oscillations: Motion of a body without any external force after initial displacement.
   • Forced Oscillations: Motion under a periodic external force.
   • Damped Oscillations: Amplitude decreases with time due to friction or resistance.
   • Resonance: When the frequency of external force matches the natural frequency, amplitude becomes maximum.
3. Simple Harmonic Motion (SHM)
   • The simplest form of oscillation where restoring force is directly proportional to displacement and directed towards the mean position.
   • Equation of SHM: F=−kxora=−ω2xF = -kx \quad \text{or} \quad a = -\omega^2 xF=−kxora=−ω2x where ω=km\omega = \sqrt{\frac{k}{m}}ω=mk​​ is the angular frequency.
4. Characteristics of SHM
   • Displacement (x): x=Asin⁡(ωt+ϕ)x = A \sin(\omega t + \phi)x=Asin(ωt+ϕ)
   • Velocity (v): v=ωA2−x2v = \omega \sqrt{A^2 – x^2}v=ωA2−x2​
   • Acceleration (a): a=−ω2xa = -\omega^2 xa=−ω2x
   • Time Period (T): T=2πωT = \frac{2\pi}{\omega}T=ω2π​
   • Frequency (f): f=1Tf = \frac{1}{T}f=T1​

Examples of Oscillatory Systems

1. Simple Pendulum:
   Time period, T=2πlgT = 2\pi \sqrt{\frac{l}{g}}T=2πgl​​ where lll is length of pendulum and ggg is acceleration due to gravity.
2. Mass-Spring System:
   Time period, T=2πmkT = 2\pi \sqrt{\frac{m}{k}}T=2πkm​​ where mmm is mass and kkk is spring constant.

Energy in SHM

• Kinetic Energy (KE): Maximum at mean position.
• Potential Energy (PE): Maximum at extreme positions.
• Total Energy (E): Constant, E=12kA2E = \frac{1}{2} k A^2E=21​kA2

Applications of Oscillations

• Clocks (pendulum clocks, quartz watches).
• Musical instruments (guitar, tabla, flute).
• Electrical oscillations in AC circuits.
• Seismology (earthquake vibrations).
• Communication systems (radio and TV transmission).

✅ Summary:
Oscillations are fundamental to understanding periodic motion in nature. SHM is the simplest form of oscillation where acceleration is proportional to displacement. Energy alternates between kinetic and potential, but the total remains constant. Oscillatory principles are widely used in science and technology.

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