# Oscillations

Periodic motion is motion that repeats in a characteristic time interval. Oscillatory motion is a special type of periodic motion in which the object moves back and forth through an equilibrium position.

Oscillatory motion is always periodic, but not all kinds of periodic motion are oscillatory. Examples:

• hands of a clock: periodic, but not oscillatory;
• circular motion: periodic, but not oscillatory;
• Earth's orbit around the Sun: periodic, but not oscillatory;
• pendulum: oscillatory.
The dynamical criterion of oscillatory motion is that the net force (or torque) must be restoring in character, that is, it must always urge the object back towards its equilibrium position.

## Prerequisites

• the fundamental quantities of kinematics: position, displacement, velocity and acceleration;
• Newton’s laws;
• the fundamentals of differential calculus.

## Learning objectives

By the end of this course, students will be able to

• compute the position, velocity and acceleration of an object in simple harmonic motion;
• employ energy considerations to compute the displacement or the speed of an object in simple harmonic motion;
• interpret oscillatory phenomena where damping is present;
• explain and analyse resonant phenomena. 