⇒ Displacement, velocity, force and acceleration are all vector quantities

⇒ Acceleration = ^{change of velocity}⁄_time

⇒ Time period = ¹⁄_frequency

⇒ Frequency = number of oscillations per second

⇒ The matural measure of angle is the radian; 2π radians = 360 degrees

⇒ Resultant force = mass x acceleration

⇒ Last year when you studied wave motion, you learnt that all types of waves require a vibrating source to produce them

• For example, vibrating or oscillating electric and magnetic fields are responsible for the production of electromagnetic waves
• There are also many examples of mechanical waves - sound waves, water waves, waves on strings or wires, and shock waves from earthquakes
• All of these waves are caused by a vibrating source

⇒ Now you are going to be studying oscillations about a fixed point

⇒ This shows three examples of mechanical oscillations - a clamped ruler, a mass on a spring, and a pendulum

• In each of these examples, we observe that the motion is repetitive about a fixed point
• The oscillating object is stationary at each end of the motion, and is moving with its maximum speed, in either direction, at the midpoint

⇒ To good approximation, these objects have these features in common:

• The force acting on the body always acts towards the equilibrium position
• The force acting on the body is proportional to its displacement from the equilibrium position

⇒ An oscillating body that satisfy both of these conditions above is said to be moving with simple harmonic motion or SHM

⇒ The two features of the motion above may be summarised in the equation:

⇒ Here k is a constant (which can be called the spring constant or the force per unit displacement)

• The significance of the minus sign is that it shows that the force (and acceleration) are in the opposite direction to the displacement
• Force, acceleration, and displacement are vectors, so we must define the direction of the displacement and motion

⇒ This image shows some important features of a simple harmonic oscillator

• When at rest, the mass hangs in its equilibrium position
• A is the amplitude of the oscillation - this is the greatest displacement of the oscillator from its equilibrium position
• When the mass is displaced downwards by x, the force acts upwards on the mass towards the equilibrium position

⇒ If you investigate the time period of a simple harmonic oscillator, you will discover that the time period does not depend on the amplitude of the oscillations, provided the amplitude is small

• If you overstretch a spring or swing a pendulum through a large angle, the motion ceases to be simple harmonic

⇒ Also see our notes on:

• Mathematical Description of SHM
• Time Period of Oscillations
• Energy in Simple Harmonic Motion
• Free, Clamped and Forced Oscillations
• Forced Oscillations