Resonance: Amplifying Oscillations at the Natural Frequency
What is the Natural Frequency?
Every oscillating system, whether it’s a swing, a guitar string, or a building, has a natural frequency.
Definition
Natural frequency
A natural frequency is a frequency at which the system naturally oscillates when not disturbed by external forces.
Resonance and Amplitude
- When an external periodic force is applied to a system at its natural frequency, the amplitude of oscillation increases significantly.
- This is because the energy from the external force is transferred efficiently to the system.
- Consider a swing being pushed.
- If you push in sync with the swing’s natural frequency, each push adds energy, making the swing go higher.
- If you push at the wrong time, the energy is not transferred efficiently, and the swing’s motion is disrupted.
Graphical Representation of Resonance
- A graph of amplitude versus driving frequency shows a sharp peak at the natural frequency.
- This peak represents the maximum amplitude achieved during resonance.
- In the absence of damping, the amplitude at resonance can theoretically become infinite.
- However, in real-world systems, damping limits the amplitude.
Energy Storage in Resonance: Efficient Energy Transfer
How Does Energy Transfer Work in Resonance?
- During resonance, energy is transferred from the external force to the oscillating system with minimal loss.
- This efficient transfer is why the amplitude increases so dramatically.
At resonance, the external force is always in phase with the system’s motion, ensuring that energy is added at the optimal point in each cycle.
The Role of Damping
Damping affects how energy is stored and transferred during resonance.
- Light Damping: The system achieves a high amplitude at resonance, and the peak is sharp.
- Heavy Damping: The amplitude is lower, and the peak is broader and shifted to a lower frequency.
- A common misconception is that damping always reduces the natural frequency.
- In reality, damping affects the amplitude and sharpness of the resonance peak, not the natural frequency itself.
