# Free and 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 oscillation as long as there are no external forces acting upon it

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

- A free oscillation always oscillates at its **resonant frequency** - The resonant frequency is the natural frequency of the system - This frequency remains constant as the system oscillates ## 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 against the resistive force responsible for decreasing the oscillations - It is sometimes known as an external **driving force**

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

- Forced oscillations are made to oscillate at the same frequency as the oscillator creating the external, periodic driving force - The system no longer oscillates at its natural frequency - Instead, it oscillates at the **driving frequency** ### Example: Child on a Swing - 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 - The swing plus the child has a fixed natural frequency, but the pushes occur at the driving frequency ## Visualizing the Frequency Difference The graph below illustrates the key distinction between free and forced oscillations. The free oscillation (at 2.0 Hz) represents the system's natural frequency, while the forced oscillation (at 0.8 Hz) shows how an external driving force can make the system oscillate at a different frequency.

## Distinguishing Between Free and Forced Oscillations ### Free Oscillation Examples **Striking a tuning fork** - When a tuning fork is struck, it will vibrate at its natural frequency - There are no other external forces acting on it after the initial strike - This is a free oscillation ### Forced Oscillation Examples **Breaking a glass with a high pitched sound** - 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 - This is a forced oscillation

Energy is transferred most efficiently when the driving frequency matches the natural frequency of the system

**The interior of a car vibrating when travelling at high speed** - The interior of the car vibrates at the same frequency as the wheels travelling over a rough surface - The vibrations from the wheels provide the external driving force - This is a forced oscillation **Playing a wind instrument (e.g., trumpet)** - The air from the player's lungs is used to sustain the vibration in the air column inside the instrument to create and hold a sound - The air column inside the instrument mimics the vibrations at the same frequency as the air forced into the mouthpiece - This is a forced oscillation ## Key Differences Summary | Feature | Free Oscillation | Forced Oscillation | |---------|-----------------|-------------------| | External forces | No external forces | Periodic external force present | | Energy input | No energy input | Continuous energy input | | Frequency | Natural frequency of system | Driving frequency (frequency of applied force) | | Energy transfer | Energy conserved (ideally) | Energy supplied to overcome damping | | Example | Struck tuning fork | Loudspeaker cone driven by electrical signal |

Avoid stating "a free oscillation is not forced to oscillate" – focus on internal vs external forces and energy transfers