# Concept of Resonance and its Characteristics

JoVE Core
Physik
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JoVE Core Physik
Concept of Resonance and its Characteristics
##### Vorheriges Video15.7: Problem Solving: Energy in Simple Harmonic Motion

Consider four pendulums tied to a string and suspended from a rigid support. Let the lengths of pendulums A and C be identical, while pendulums B and D have different lengths.

When pendulum A is displaced, it oscillates with a natural frequency, and the energy from pendulum A is transferred to the other pendulums, forcing them to oscillate with a driving frequency.

The given expression relates the amplitude with natural and driving frequency.

On close observation, it is found that pendulums B and D oscillate with driving frequencies quite different from their natural frequencies, resulting in smaller amplitudes.

In contrast, the driving frequency of the pendulums with identical lengths is equal to their natural frequency, causing the amplitude to increase gradually with each oscillation. This condition—when the driving frequency equals the natural frequency—is called resonance.

In a damped harmonic oscillator, under the resonance condition, the amplitude can be altered depending on the damping force. The amplitude is large and narrow for small damping, while it is smaller for heavy damping.

## Concept of Resonance and its Characteristics

If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not immune to resonance. Despite highly engineered shock absorbers, which ordinarily convert mechanical energy to thermal energy almost as fast as it comes in, speed bumps still cause a large-amplitude oscillation. On gravel roads that are corrugated, the bumps are very noticeable if the car travels at a wrong speed, whereas at other speeds, the bumps are hardly felt.

These features of driven harmonic oscillators apply to a huge variety of systems. When a radio is tuned, for example, its resonant frequency is adjusted so that it only oscillates to the desired station's broadcast (driving) frequency. The more selective the radio is in discriminating between two stations, the smaller is its damping. In all of these cases, the efficiency of energy transfer from the driving force into the oscillator is best observed at resonance.