Resonance

Definition

Resonance is a phenomenon that occurs when a system is driven by an external force at a frequency that matches the system's natural or resonant frequency, resulting in a dramatic increase in the amplitude of the system's oscillations.

5 Must Know Facts For Your Next Test

1. Resonance occurs when the frequency of the driving force matches the natural frequency of the system, causing a large increase in the amplitude of oscillations.
2. The quality or sharpness of the resonance peak is determined by the amount of damping in the system, with less damping resulting in a narrower and taller resonance peak.
3. Resonance is a fundamental concept in physics and engineering, and it is observed in a wide range of systems, from mechanical oscillators to electrical circuits and even in the human body.
4. Resonance can be both beneficial and detrimental, as it can be used to amplify desired signals, but it can also lead to catastrophic failures if the driving frequency matches the natural frequency of a structure.
5. Understanding and controlling resonance is crucial in the design of various systems, from bridges and buildings to musical instruments and electronic devices.

Review Questions

• Explain the relationship between the natural frequency of a system and the phenomenon of resonance.
  • Resonance occurs when the frequency of the driving force applied to a system matches the system's natural frequency. When this happens, the system's oscillations are amplified dramatically, as the driving force is in sync with the system's natural vibrations. The natural frequency is a fundamental property of the system, determined by its physical characteristics, such as mass, stiffness, and damping. By understanding the natural frequency of a system, engineers and scientists can predict when resonance will occur and take steps to either avoid or harness it, depending on the application.
• Describe how the amount of damping in a system affects the quality or sharpness of the resonance peak.
  • The amount of damping in a system plays a crucial role in determining the quality or sharpness of the resonance peak. Systems with low damping, such as a lightly-damped mechanical oscillator, will exhibit a narrow and tall resonance peak, where the amplitude of oscillations increases dramatically at the natural frequency. Conversely, systems with high damping, such as those with significant friction or energy dissipation, will have a broader and shorter resonance peak. The sharper the resonance peak, the more sensitive the system is to the driving frequency, and the more potential there is for both beneficial and detrimental effects of resonance.
• Evaluate the importance of understanding and controlling resonance in the design of various systems and structures.
  • Understanding and controlling resonance is crucial in the design of a wide range of systems and structures, from mechanical and electrical devices to buildings and bridges. Resonance can be used beneficially to amplify desired signals, such as in the design of musical instruments or electronic filters. However, if the driving frequency of a system matches the natural frequency, it can lead to catastrophic failures, as seen in the case of the Tacoma Narrows Bridge collapse. Engineers must carefully consider the natural frequencies of their designs and either avoid resonance by ensuring the driving frequencies are sufficiently different, or harness resonance to their advantage. Failure to account for resonance can result in severe consequences, making it a critical concept for designers and scientists to fully comprehend.

Related terms

Natural Frequency: The frequency at which a system naturally vibrates or oscillates when it is disturbed and allowed to freely move.

Damping: The process of reducing the amplitude of oscillations in a system, typically due to friction or other dissipative forces.

Forced Oscillation: The oscillation of a system caused by an external, time-dependent force or driver, as opposed to the system's natural vibrations.