Oscillations

What is the difference between
free and forced oscillations?

An oscillation that takes place in the absence of any variable external force or any kind of resistive force is called a free oscillation.

An oscillation taking place under the action of periodic external forces is called a forced oscillation.

Examples of the free oscillations

Characteristics of the oscillations

The time period is the time taken for one complete oscillation.
Unit: second

𝑻𝑻= 𝒕 𝑵 𝒕𝒕 𝒕 𝑵 𝑵𝑵 𝒕 𝑵

𝑷𝒆𝒓𝒊𝒐𝒅= 𝒕𝒊𝒎𝒆 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒐𝒔𝒄𝒊𝒍𝒍𝒂𝒕𝒊𝒐𝒏𝒔

The frequency is the number of complete oscillations per unit time.
Unit: Hz or s-1

𝒇𝒇= 𝑵 𝒕 𝑵𝑵 𝑵 𝒕 𝒕𝒕 𝑵 𝒕

𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚= 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒐𝒔𝒄𝒊𝒍𝒍𝒂𝒕𝒊𝒐𝒏𝒔 𝒕𝒊𝒎𝒆

The angular frequency is found by multiplying f by 2π (ω = 2π·f)

The amplitude is defined as the maximum displacement from the equilibrium position.
Symbol: A or xm. Unit: metre

A displacement-time graph to show the meanings of amplitude and period.

Investigation the dependence of the oscillation period of the pendulum on various parameters.

- know different types of oscillating systems;
- explain the causes of oscillations in various oscillating systems;
- investigate the dependence period of the oscillation of the pendulum on various parameters.

Mass-spring system

Simple
Pendulum

The period of oscillation of a simple pendulum is independent of its mass. It is also independent of the amplitude for small oscillations.

The period of oscillations is independent of amplitude for a mass-spring system. The period of oscillations of amplitude a mass-spring system is also independent of gravity.