What's the difference between forced and natural frequency?

Forced frequency is imposed by an external force, while natural frequency is inherent to a system's physical properties.

Forced frequency refers to the frequency at which an external force is applied to a system. This could be anything from a push on a swing to an electrical signal in a circuit. The system will respond to this frequency, but it may not do so efficiently if the forced frequency is different from its natural frequency. For example, if you push a swing at a frequency that's different from its natural frequency, it won't swing as high as it could. This is because the system can't absorb and store the energy from the force as efficiently.

On the other hand, natural frequency is the frequency at which a system would oscillate if it were not being driven by an external force. It's determined by the physical properties of the system, such as its mass and stiffness. For example, a guitar string has a natural frequency that depends on its length, tension, and the material it's made from. When you pluck the string, it vibrates at its natural frequency, producing a specific pitch.

In many physical systems, the response is greatest when the forced frequency matches the natural frequency. This is known as resonance. It's why a glass can shatter when a singer hits the right note, or why a bridge can collapse if soldiers march across it in step. The energy from the force is absorbed and stored more efficiently, causing the amplitude of the oscillation to increase.

However, resonance can also be destructive, as in the examples above. Engineers need to take it into account when designing structures, to ensure they won't fail under certain conditions. They may use damping, which is a way of dissipating energy, to prevent resonance from occurring. For example, car suspension systems use shock absorbers to damp the oscillations and provide a smoother ride.

In summary, forced frequency is the frequency at which an external force is applied to a system, while natural frequency is inherent to the system's physical properties. The interaction between these two frequencies can lead to resonance, which can be both useful and potentially destructive.