Chapter 7.3, Problem 1.5SP

Resonance

Consider an undamped system exhibiting simple harmonic motion. In the real world, we never truly have an undamped system; -some damping always occurs. For theoretical purposes, however, we could imagine a spring-mass system contained in a vacuum chamber. With no air resistance, the mass would continue to move up and down indefinitely.

The frequency of the resulting motion, given by $f=\frac{1}{T}=\frac{\omega }{2\pi }$ , is called the natural frequency of the system. If an external force acting on the system has a frequency close to the natural frequency of the system, a phenomenon called resonance results. The external forte reinforces and amplifies the natural motion of the system.

5. Another real-world example of resonance is a singer shattering a crystal wineglass when she sings just the right note. When someone taps a crystal wineglass or wets a finger and runs it around the rim, a tone can be heard. That note is created by the wineglass vibrating at its natural frequency. If a singer then sings that same note at a high enough volume, the glass shatters as a result of resonance.

The TV show Mythbusters aired an episode on this phenomenon. Visit this website (http:// www.openstaxcollege.org/l/20_glass) to learn more about it. Adam Savage also described the experience. Watch this video (http://www.openstaxcollege.org/l/20_glass2) for his account.