# Introduction

The world is full of things that move. The motion of physical systems can be classified into two broad categories - translatory and vibratory or oscillatory. If the position of a body varies linearly with time, its motion is translatory, e.g., a train moving on a straight track or a ball rolling on the ground. A motion that repeats itself in equal intervals of time is called periodic motion, e.g. the motion of the hands of a clock. If a particle in periodic motion moves back and forth over the same path, its motion is called vibratory or oscillatory. Some examples of oscillatory motion are the oscillation of the hands of a walking person, the balance wheel of a watch, the bob of a pendulum clock, a mass attached to a spring, the prongs of a tuning fork, the piston of an automobile engine, etc.

Oscillations may be very complex, such as those of a piano string or those of the earth during an earthquake. It may be remarked that mechanical systems are not the only ones that can oscillate. The atoms in a solid vibrate. The electrons in a radiating or receiving antenna are in oscillation. A tuned circuit in a radio can oscillate electromagnetically. Radiowaves, microwaves and visible light are simply oscillating electric and magnetic fields. Thus, the study of oscillations is essential for the understanding of various physical systems-mechanical, acoustical, electrical and atomic.

In this chapter, we will study the simplest and smoothest type of oscillatory motion, namely, simple harmonic motion (usually designated as SHM). Among the various types of oscillatory motions, SHM is of central importance for three basic reasons:

1. the oscillation of all physical systems is simple harmonic or a close approximation to it, if the oscillation is not too violent;
2. the study of SHM is essential for the understanding of wave motion;
3. we will learn in higher classes that complex oscillations, e.g. those of a piano string, can be expressed as a combination of harmonic motions.