How do you distinguish between free and forced oscillations?

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

Free oscillations, also known as natural oscillations, are oscillations that occur in a system when it is set into motion and then left to oscillate without any external influences. These oscillations are determined by the system's own natural frequency, which is a characteristic of the system itself and depends on factors such as its mass and stiffness. For example, if you pluck a guitar string and let it vibrate, it will oscillate at its natural frequency. This is a free oscillation. This is a free oscillation. For more on the basics of oscillations, explore the basics of simple harmonic motion (SHM).

Forced oscillations, on the other hand, occur when a system is subjected to an external periodic force. This external force 'forces' the system to oscillate at the frequency of the force, rather than at its natural frequency. The amplitude and phase of the oscillations are determined by the frequency and amplitude of the external force. For instance, if you continuously push a child on a swing at regular intervals, the swing will oscillate at the frequency of your pushes. This is a forced oscillation.

It's important to note that in forced oscillations, if the frequency of the external force matches the natural frequency of the system, a phenomenon known as resonance occurs. This can cause the amplitude of the oscillations to increase dramatically, which can potentially lead to destructive consequences. For example, if wind causes a bridge to oscillate at its natural frequency, the bridge could collapse. Detailed explanations on energy in SHM and resonance can be found on our pages about energy in SHM and resonance.

In summary, the key difference between free and forced oscillations lies in the presence or absence of an external force. Free oscillations occur naturally without any external influence and oscillate at the system's natural frequency, while forced oscillations are driven by an external periodic force and oscillate at the frequency of this force. To understand how damping affects oscillations, consider reading about damping in SHM, which further elucidates how external forces can alter the natural oscillation of systems.