# 13.9 Free & Forced Oscillations

## Free & Forced Oscillations

#### Free Oscillations

• Free oscillations occur when there is no transfer of energy to or from the surroundings
• This happens when an oscillating system is displaced and then left to oscillate

• In practice, this only happens in a vacuum. However, anything vibrating in air is still considered a free vibration as long as there are no external forces acting upon it
• Therefore, a free oscillation is defined as:

An oscillation where there are only internal forces (and no external forces) acting and there is no energy input

• A free vibration always oscillates at its resonant frequency

#### Forced Oscillations

• In order to sustain oscillations in a simple harmonic system, a periodic force must be applied to replace the energy lost in damping
• This periodic force does work on the resistive force decreasing the oscillations
• It is sometimes known as an external driving force

• These are known as forced oscillations (or vibrations), and are defined as:

Oscillations acted on by a periodic external force where energy is given in order to sustain oscillations

• Forced oscillations are made to oscillate at the same frequency as the oscillator creating the external, periodic driving force
• For example, when a child is on a swing, they will be pushed at one end after each cycle in order to keep swinging and prevent air resistance from damping the oscillations
• These extra pushes are the forced oscillations, without them, the child will eventually come to a stop

#### Worked example

State whether the following are free or forced oscillations:

(i) Striking a tuning fork

(ii) Breaking a glass from a high pitched sound

(iii) The interior of a car vibrating when travelling at a high speed

(iv) Playing the clarinet

(i) Striking a tuning fork

This is a free vibration. When a tuning fork is struck, it will vibrate at its natural frequency and there are no other external forces

(ii) Breaking a glass from a high pitched sound

This is a forced vibration. The glass is forced to vibrate at the same frequency as the sound until it breaks. The frequency of the high-pitched sound is the external driving frequency

(iii) The interior of a car vibrating when travelling at a particular speed

This is a forced vibration. The interior of the car vibrates at the same frequency as the wheels travelling over a rough surface at a high speed

(iv) Playing the clarinet

This is a forced vibration. The air from the player's lungs is used to sustain the vibration in the air column in a clarinet to create and hold a sound. The air column inside the clarinet mimics the vibrations at the same frequency as the air forced into the mouthpiece of the clarinet (the reed).

#### Exam Tip

Avoid writing 'a free oscillation is not forced to oscillate'. Mark schemes are mainly looking for a reference to internal and external forces and energy transfers

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