# PHY C13: Oscillations

Today’s topic:

• Oscillations
• Free oscillations
• Motion of an Oscillator

Let’s go!

What are oscillations?
To-&-fro motion between 2 limits.

What is a single oscillation?
One complete movement from starting/rest position, to the maximum displacement in both directions, then back to the starting position.

Oscillations can be divided into certain categories & subcategories:

Let’s look at Free Oscillations first.

What is a free oscillation?
The oscillation of a system with no externally applied stimuli.

It oscillates with:

• Constant amplitude
• Constant total energy (no energy lost)

What is an oscillator?
A mechanical or electronic device that works on the principles of oscillation (periodic fluctuation between 2 positions based on changes in energy).

An oscillator utilising simple harmonic oscillation is a harmonic oscillator.

For example:

• Clocks
• Metal detectors

Motion in Free Oscillation
In real life, most oscillations do NOT oscillate freely (there is usually some loss of energy).

However, some can be approximated to have free oscillations & simple harmonic motion.
We will look at 2 examples:

• a pendulum (with an angle less than 10°)
• a vertical weighted spring (where extension does not exceed proportionality limit)

& see how their motion can be represented.

 Real Motion Pendulum Spring Sinusoidal Graph Mapped onto a Circle See here for a more in-depth analysis of these examples as simple harmonic motion.

Components of free oscillation

 Aspect Definition Denoted by: In Free Oscillation: Displacement Vector distance of a particle from its equilibrium position x Measured in cm or m Varies with time Amplitude Maximum displacement from rest position x0 Measured in cm or m Stays constant Period Time taken for one complete oscillation T Measured in s Stays constant Frequency Number of oscillations in one second f = 1/T Measured in Hz Stays constant Angular Frequency Angular displacement (in radian) per unit time This angle is the angle travelled when an oscillation is MAPPED onto a CIRCLE ω = 2πf Measured in rad s-1 Stays constant Phase Difference Difference in time or angle of oscillation between 2 identical oscillating objects φ Measured in s OR °