A metal sphere with a mass of 4.00 kg oscillates at the end of a vertical spring with a spring constant of 2.20 x 104 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N s/m.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
icon
Concept explainers
Topic Video
Question
A metal sphere with a mass of 4.00 kg oscillates at the end of a vertical spring with a spring constant of 2.20 x 104 N/m. The
motion is damped by air resistance, and the damping coefficient is b = 3.00 N · s/m.
(a) What is the frequency (in Hz) of the damped oscillation?
11.802
Hz
(b) By what percentage does the amplitude of the oscillation decrease in each cycle?
3.1
%
(c) Over what time interval (in s) does the energy of the system drop to 3.00% of its initial value?
4.68
S
(d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is
150 N · s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the
represented by b
atmosphere of Venus.
What is the frequency (in Hz) of the damped oscillations?
11.419
Hz
What is the percentage decrease in amplitude in each cycle?
74.45
Follow the same steps as in part (b), only use the new value of b. Remember the angular frequency has now changed as
well. Be sure to express your answer as a percentage, and not a fraction. %
What is the time interval (in s) for the energy to drop to 3.00% of its initial value?
Transcribed Image Text:A metal sphere with a mass of 4.00 kg oscillates at the end of a vertical spring with a spring constant of 2.20 x 104 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N · s/m. (a) What is the frequency (in Hz) of the damped oscillation? 11.802 Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? 3.1 % (c) Over what time interval (in s) does the energy of the system drop to 3.00% of its initial value? 4.68 S (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is 150 N · s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the represented by b atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? 11.419 Hz What is the percentage decrease in amplitude in each cycle? 74.45 Follow the same steps as in part (b), only use the new value of b. Remember the angular frequency has now changed as well. Be sure to express your answer as a percentage, and not a fraction. % What is the time interval (in s) for the energy to drop to 3.00% of its initial value?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Simple Harmonic Motion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON