Question 3 Two objects of equal mass on an effectively frictionless horizontal air track are held between rigid supports by three identical springs, as shown in the figure below. The displacements from equilibrium along the line of the springs are described by coordinates xA and xB. If either of the masses is clamped, the period T for one complete vibration of the other is 3 sec. lellll ell (a) write out the equations of motion for the system. (b) If both objects are free, what are the periods of the two nomal modes of the system? At t = 0, mass A is at its normal resting position and object B is pulled aside a distance of 5 cm. The masses are released from rest at this instant. (c) write an equation for the subsequent displacement of each object as a function of time. (d) What is the time (in seconds) characterises the periodic transfer of the motion from B to A and back again?
Question 3 Two objects of equal mass on an effectively frictionless horizontal air track are held between rigid supports by three identical springs, as shown in the figure below. The displacements from equilibrium along the line of the springs are described by coordinates xA and xB. If either of the masses is clamped, the period T for one complete vibration of the other is 3 sec. lellll ell (a) write out the equations of motion for the system. (b) If both objects are free, what are the periods of the two nomal modes of the system? At t = 0, mass A is at its normal resting position and object B is pulled aside a distance of 5 cm. The masses are released from rest at this instant. (c) write an equation for the subsequent displacement of each object as a function of time. (d) What is the time (in seconds) characterises the periodic transfer of the motion from B to A and back again?
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter1: Units And Measurement
Section: Chapter Questions
Problem 83AP: A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of...
Related questions
Concept explainers
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Topic Video
Question
Coupled oscillations question
Transcribed Image Text:W
Document1 - Microsoft Word (Product Activation Failed)
File
Home
Insert
Page Layout
References
Mailings
Review
View
a ?
W
A
A Find -
% Cut
- A A
E- E - F
章 T
Aal
Calibri (Body) - 11
Aa
AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL
E Copy
ae Replace
Paste
B I U
U - abe x, x²
A
ab
A
I Normal
I No Spaci. Heading 1
Change
.
Heading 2
Title
Subtitle
Format Painter
Styles - Select -
Clipboard
Font
Paragraph
Styles
Editing
L
• 2. 1:.
I' 2: 1 : 3:1
• 4.I 5.1' 6.1'7
I'8: 1 9 ' 10.L· 11: 1 ' 12.'13 · L 14: 1· 15.1A L'17:1 18
Question 3
Two objects of equal mass on an effectively frictionless horizontal air track are held between rigid
supports by three identical springs, as shown in the figure below. The displacements from equilibrium
along the line of the springs are described by coordinates XA and xB. If either of the masses is clamped, the
period T for one complete vibration of the other is 3 sec.
k
k
k
e
elle
elll
A
в
(a) write out the equations of motion for the system. (b) If both objects are free, what are the periods of
the two normal modes of the system? At t = 0, mass A is at its normal resting position and object B is
pulled aside a distance of 5 cm. The masses are released from rest at this instant. (c) write an equation for
the subsequent displacement of each object as a function of time. (d) What is the time (in seconds)
characterises the periodic transfer of the motion from B to A and back again?
ull
05:40 PM
2021-06-22 Page: 1 of 1
国 昆言
E E E E
+
Words: 0
100% -
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
Knowledge Booster
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.Recommended textbooks for you
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College
Foundations of Astronomy (MindTap Course List)
Physics
ISBN:
9781337399920
Author:
Michael A. Seeds, Dana Backman
Publisher:
Cengage Learning
University Physics Volume 1
Physics
ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University
College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College
Foundations of Astronomy (MindTap Course List)
Physics
ISBN:
9781337399920
Author:
Michael A. Seeds, Dana Backman
Publisher:
Cengage Learning