Understanding Resonance: Causes and Effects in Oscillating Systems

[Harmony]

Why does an oscillating system under resonance oscillate with the largest amplitude? And why does resonance occur when the driving frequency match the natural frequency? Can resonance occur at frequency other than natural frequency?

 

[twobagger]

Why does an oscillating system under resonance oscillate with the largest amplitude?

Because, in absence of a damping force, the driving force and the velocity of the system have the exact same direction. Therefore, a positive amount of work is constantly being done, and therefore, the mechanical energy of the system is increasing.
So, the amplitude will, in absence of a damping force, increase without limit.

And why does resonance occur when the driving frequency match the natural frequency?

Because, since the driving frequency matches the natural frequency, the direction of the driving force matches the direction of the oscillating system's frequency.

Can resonance occur at frequency other than natural frequency?

I'm pretty sure it can't.

 

[m2003]

I can provide an explanation for the phenomena of resonance in oscillating systems. Resonance occurs when a driving force or external force is applied to an oscillating system at the same frequency as its natural frequency. This causes the system to oscillate with the largest amplitude.

The natural frequency of an oscillating system is the frequency at which it naturally vibrates or oscillates without any external force applied. This frequency is determined by the physical properties of the system, such as its mass, stiffness, and damping. When the driving frequency matches the natural frequency, the system is able to absorb and store the energy from the external force, resulting in a larger amplitude of oscillation.

This can be understood through the concept of constructive interference. When the driving frequency matches the natural frequency, the oscillations from the external force and the system's natural oscillations are in phase, meaning they align and add together to create a larger amplitude. This is similar to how pushing someone on a swing at the right time can make them go higher.

Additionally, resonance can only occur at the natural frequency because any other frequency would result in destructive interference, where the oscillations from the external force and the system's natural oscillations are out of phase and cancel each other out. This would result in a smaller amplitude of oscillation.

In certain cases, it is possible for resonance to occur at frequencies other than the natural frequency. This is known as forced resonance and can happen when the driving frequency is a multiple of the natural frequency. In this case, the system experiences a series of smaller resonances, known as subharmonics, which can still result in larger amplitudes of oscillation.

In conclusion, resonance in oscillating systems occurs when the driving frequency matches the natural frequency, resulting in the largest amplitude of oscillation due to constructive interference. Other frequencies can also cause resonance, but only when they are multiples of the natural frequency. Understanding the causes and effects of resonance is important in various fields of science and engineering, such as in the design and operation of musical instruments, bridges, and electronic circuits.