1. Introduction
Introduction to oscillatory motion and periodic systems
What is Oscillatory Motion?
Oscillatory motion studies repetitive motion about an equilibrium position.
It extends concepts from linear motion to systems that vibrate or swing back and forth.
Key concepts include simple harmonic motion (SHM), period, frequency, and amplitude.
Why Study Oscillations?
It explains how pendulums swing, springs vibrate, and musical instruments produce sound.
It is fundamental to engineering, acoustics, structural design, and electronics.
Applications
- Clock mechanisms and timekeeping
- Shock absorbers and suspension systems
- Musical instruments and acoustics
- Earthquake engineering and seismology
Prerequisites
- Newton's laws of motion
- Energy conservation
- Trigonometry and calculus
- Understanding of forces and acceleration
Module Breakdown
- Simple Harmonic Motion: Defining equation, relationship to circular motion, period and frequency
- Energy in SMH: Kinetic and potential energy variations, total energy conservation
- Pendulums: Simple pendulum, physical pendulum, period dependence
- Distributed Mass Pendulum: Pendulums with extended mass distributions, moment of inertia effects
- Damping: Light, critical, and heavy damping, exponential decay of amplitude
- Forced Oscillations: Driving forces, resonance, amplitude-frequency response