Oscillations Short Notes | Class 11th | SHM

Hello Learner's! Today, we embark on a fascinating journey into the rhythmic heartbeat of the physical world — a journey through the captivating realm of oscillations. As we deliver into this chapter, we will unravel the secrets of motion.

Our exploration today is not merely a scientific expedition; it is an odyssey into the very fabric of nature. From the elegant simplicity of a swinging pendulum to the complex interplay of forces in a spring-mass system, each concept we encounter paints a vivid portrait of the laws that govern motion.

Thank you for joining me on this scientific exploration. Without further delay, let the journey into the captivating world of oscillations commence.

Oscillations

Introduction

• Definition: Oscillation refers to the repetitive motion of a body about a central position, typically a position of equilibrium.

• Examples: Simple pendulum, mass-spring system, vibrating guitar string, etc.

   

• Periodic Motion:

  • Definition: Motion that repeats itself at regular intervals.
  • Example: A swinging pendulum, where the pendulum bob oscillates back and forth in a regular pattern. 
    

Simple Harmonic Motion (SHM)

• Definition: A special type of oscillatory motion in which a particle moves to and fro about a fixed point and the acceleration is directly proportional to the displacement and is always directed towards the mean position.

Characteristics of SHM:

1. Amplitude (A): Maximum displacement of the particle from the mean position.
2. Time Period (T): Time taken to complete one oscillation.
   • Relation with frequency (f): $f=\frac{1}{T}$
3. Frequency (f): Number of oscillations per unit time.
   • Relation with angular frequency ($\omega$): $\omega =2\pi f=\frac{2\pi }{T}$
4. Phase: Describes the position of the particle at any instant.
5. Equation of Motion: $x=A\sin (\omega t+\varphi )$, where $x$ is the displacement at time $t$, $\omega$ is the angular frequency, and $\varphi$ is the phase constant.

Simple Pendulum

• Definition: A heavy point mass (bob) suspended by a light and inextensible string.

Characteristics:

1. Time Period (T): $T=2\pi \sqrt{\frac{L}{g}}$, where $$ is the length of the pendulum and $$ is the acceleration due to gravity.

Spring-Mass System

• Hooke's Law: $F=-kx$, where $F$ is the restoring force, $k$ is the spring constant, and $x$ is the displacement from equilibrium.

• Time Period (T): $T=2\pi \sqrt{\frac{m}{k}}$

• ​, where $m$ is the mass of the object.

Damping

• Damping Force: A force opposing the motion of an oscillating object.

• Types of Damping:

  1. Underdamping: Oscillations decrease gradually.
  2. Overdamping: Oscillations die out without crossing the equilibrium position.
  3. Critical Damping: The system returns to equilibrium as quickly as possible without oscillating.

Forced Oscillations and Resonance

• Forced Oscillation: A periodic external force applied to a system undergoing oscillations.

• Resonance: The amplitude of oscillations becomes maximum when the frequency of the applied force is equal to the natural frequency of the system.

Waves

• Definition: A disturbance that propagates through space and time, usually with transference of energy.

• Types of Waves:

  1. Mechanical Waves: Require a medium (e.g., sound waves).
  2. Electromagnetic Waves: Can travel through a vacuum (e.g., light waves).

Characteristics:

1. Amplitude (A): Maximum displacement of a particle in the wave.
2. Wavelength ($$): Distance between two consecutive points in phase.
3. Frequency (f): Number of oscillations per unit time.
   • Relation with velocity (v) and wavelength: $v=f\lambda$

Superposition Principle

• Principle: When two or more waves meet at a point, the resultant displacement at that point is the vector sum of the displacements of individual waves.

These are the key concepts related to oscillations in Class 11 Physics. Understanding these principles will provide a solid foundation for more advanced topics in physics.

 

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