Periodic force applied to a system with a natural frequency produces resonanceThe connection between force and motion is more complex for harmonic motion than it is for linear motion. The difference is that forces can be periodic. A periodic force is a force that repeats in cycles—like the repeated push–wait–push–wait–push—that you use to get a swing going. Of course, Newton’s laws still apply, but the frequency of a periodic force is a new variable that can make a huge difference. When the frequency of the force matches a system’s natural frequency, even a small force can produce a surprisingly large oscillation. The effect is called resonance, and it is found throughout both nature and technology. Read the text aloud
Think about pushing someone on a swing. A swing is a pendulum and it has a natural frequency. To create a large amplitude you supply a small push every time the swing reaches the end of its cycle. In the language of physics, your repetitive pushes are a periodic force at the natural frequency of the swing. Over many pushes, the swing builds up a large amplitude of motion even though any single push does not do much by itself. Read the text aloud
When the frequencies of the force and the system are matched, each push comes at just the right moment and the amplitude increases dramatically. This behavior is called resonance. Resonance occurs when the frequency of a periodic force matches the natural frequency of a system. Although the physical laws are the same as for linear motion, resonance is a unique behavior of harmonic motion. Read the text aloud
Examples of systems in and out of resonance
A resonant system accumulates energy with every cycle of the applied force. A system in resonance is a very efficient energy accumulator. This is useful in technology because the energy is concentrated at the natural frequency! If you want a musical instrument to have a vibration of 100 Hz, you create something physical that has a natural frequency of 100 Hz. By doing this, only vibrations at a frequency of 100 Hz will have a large amplitude. This is the principle behind musical instruments and modern communications technologies. When you tune the FM stereo in your car what you are doing is adjusting the resonance frequency of your car’s receiver to match the frequency transmitted by a particular station. Read the text aloud
In 1940, the Tacoma Narrows Bridge in Washington State vibrated and twisted amid 40 mph winds, resulting in its dramatic collapse caught on video (at left). Was this a real-world example of forced resonance, where the oscillatory frequency of the wind matched the natural frequency of the bridge? Watch the video and decide for yourself. Read the text aloud Show Collapse of the Tacoma Narrows Bridge
Which of the following is not an example of resonance?
  1. a trumpet player vibrating his lips to make a note
  2. a child bouncing a ball up and down
  3. a singer singing a specific note for a glass to vibrate and break
  4. a person pushing another on a swing set

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