Free oscillations occur naturally without any external force, while forced oscillations are driven by an external periodic force.

Free oscillations, also known as natural oscillations, arise in a system when it is set into motion and then allowed to oscillate independently of external influences. The characteristics of these oscillations are determined by the system’s natural frequency, a property intrinsic to the system that depends on factors such as mass and stiffness. For example, when you pluck a guitar string and permit it to vibrate freely, it will oscillate at its natural frequency. This phenomenon exemplifies free oscillation. To delve deeper into the fundamentals of oscillations, feel free to explore our resources.

In contrast, forced oscillations occur when a system is subjected to an external periodic force. In this case, the external force compels the system to oscillate at the frequency of that force, rather than at its own natural frequency. The amplitude and phase of the resulting oscillations depend on both the frequency and amplitude of the external force. For instance, if you regularly push a child on a swing, the swing will oscillate at the frequency of your pushes, illustrating a forced oscillation.

It is crucial to understand that when the frequency of the external force aligns with the natural frequency of the system, a phenomenon known as resonance can occur. This can lead to a significant increase in the amplitude of the oscillations, which may result in destructive outcomes. For example, if wind causes a bridge to oscillate at its natural frequency, it could potentially collapse. For more detailed explanations about energy in simple harmonic motion (SHM) and resonance, refer to our dedicated pages.

In summary, the primary distinction between free and forced oscillations lies in the presence or absence of an external force. Free oscillations occur naturally without any external influence and resonate at the system’s natural frequency, whereas forced oscillations are driven by an external periodic force and oscillate at that force’s frequency. To understand how damping impacts oscillations, we encourage you to read about it further, as it elucidates how external forces can modify the natural oscillation behavior of systems.