No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. The response is simply out of proportion to the stimulus. Of course, we are just creating imagery to focus attention. However, anyone who has seen the four-minute film clip of the Tacoma Narrows Bridge, Tacoma, Washington, twisting in the wind and collapsing in 1940 would need no additional metaphors for resonance, the phenomenon responsible for such a ruinous end to a magnificent work of engineering.
Resonance is quantized within the driven damped oscillator.
A linear, damped oscillator is driven with a sinusoidal input having a variable angular frequency. The response of the system is observed as a function of the driving input frequency. The frequency for which the response is greatest is called the resonant frequency , a frequency at which the magnitude of the system's response can be far larger than the magnitude of the input driving force. We distinguish two cases of resonance. If damping is assumed to be zero, the system is a fiction, since even at supercooled temperatures, friction does not disappear entirely.