
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
4. In the real world, there is always some damping. However, if the damping force is weak, and the external force is strong enough, real-world systems can still exhibit resonance. One of the most famous examples of resonance is the collapse of the Tacoma Narrows Bridge on November 7, 1940. The bridge had exhibited strange behavior ever since it was built. The roadway had a strange “bounce” to it. On the day it collapsed, a strong Windstorm caused the roadway to twist and ripple violently. The bridge was unable to withstand these forces and it ultimately collapsed. Experts believe the windstorm exerted forces on the bridge that were very close to its natural frequency, and the resulting resonance ultimately shook the bridge apart.
This website (http://www.openstaxcollege.org/l/20_TacomaNarrow) contains more information about the collapse of the Tacoma Narrows Bridge.
During the short time the Tacoma Narrows Bridge stood, it became quite a tourist attraction. Several people were on site the day the bridge collapsed, and one of them caught the collapse on film. Watch the video (http//www.openstaxcollege.org/l/20_TacomaNarr02) to see the collapse.

Want to see the full answer?
Check out a sample textbook solution
Chapter 7 Solutions
Calculus Volume 3
Additional Math Textbook Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Elementary Statistics (13th Edition)
University Calculus: Early Transcendentals (4th Edition)
Elementary Statistics: Picturing the World (7th Edition)
Calculus: Early Transcendentals (2nd Edition)
Thinking Mathematically (6th Edition)
- II Consider the following data matrix X: X1 X2 0.5 0.4 0.2 0.5 0.5 0.5 10.3 10 10.1 10.4 10.1 10.5 What will the resulting clusters be when using the k-Means method with k = 2. In your own words, explain why this result is indeed expected, i.e. why this clustering minimises the ESS map.arrow_forwardX Acellus | Student admin192c.acellus.com go 0:0 Hannah wants to have concrete stairs for her backdoor. How much concrete will be needed to build the stairs? 20 cm 70 cm 30 cm 15 cm 10 cm 45 cm cm 70 cm GIF 自 لاarrow_forwardwhy the answer is 3 and 10?arrow_forward
- 1 Hannah wants to have concrete stairs for her backdoor. How much concrete will be needed to build the stairs? 70 cm 30 cm 15 cm 10 cm 10 cm 20 cm 45 cm cm³ GIF GIF/ 2 3 4 qwe asdf 5 6 自 yu ty u 8 ghjk 9 P Z X C cv b vbnm ×arrow_forwardPS 9 Two films are shown on screen A and screen B at a cinema each evening. The numbers of people viewing the films on 12 consecutive evenings are shown in the back-to-back stem-and-leaf diagram. Screen A (12) Screen B (12) 8 037 34 7 6 4 0 534 74 1645678 92 71689 Key: 116|4 represents 61 viewers for A and 64 viewers for B A second stem-and-leaf diagram (with rows of the same width as the previous diagram) is drawn showing the total number of people viewing films at the cinema on each of these 12 evenings. Find the least and greatest possible number of rows that this second diagram could have. TIP On the evening when 30 people viewed films on screen A, there could have been as few as 37 or as many as 79 people viewing films on screen B.arrow_forwardskip A swimming pool plan has concrete stairs leading down into the shallow end How much concrete will be needed to build the stairs? Bift 9 ft 2 ft 1 ft 9 ft 2 ft 5 ft [ ? ] ft³arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
