Coupled Flarmonic Oscillators X2 : 0 ) Write down the 2nd law for each of the masses. Use coordinates x, aud x, for m and M, and i,, ×2 and a, az. timt: the force from the ferce from spring 2 &on m | on m'only depends but on X,, spring depand s on (x2-x,)
Coupled Flarmonic Oscillators X2 : 0 ) Write down the 2nd law for each of the masses. Use coordinates x, aud x, for m and M, and i,, ×2 and a, az. timt: the force from the ferce from spring 2 &on m | on m'only depends but on X,, spring depand s on (x2-x,)
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)...
Related questions
Question
![Coupled
Harmonic
Oscillators
X2 :0
eeeee
Leeee NM
) Write down the 2nd law for each of the masses.
Use coordinates x, aud x, for m and M, and i,, *2 and a, a2.
Hirnt: the force from spring I on monly depends
on x, , but
the ferce from spring 2 on m
depand s
on (x2-x,)
two differantial
2) To simplify, let k, -k,k and m-M. Rewrite
egg equatious from i) right above each other.
your
3) Detine two new variables, X (Greek"chi") - x,+X2 and Ax = X,-x 2
two di ferential equations to produce
Then add and subtract
your
very simple (harmanic) ones.
4) Write down the solutiou to bothe equations using
Wask+2k2 ond evefficients A, B, C, and D
two new ,
but
w. :
un
5) Now assune k-10k2 (this means that the two masses are
"weakly coupled"). Also assume X,(0) = -10cm, x,(0)=0, xz (0)= o,
x,(0)=0. Solve for A,B, C, D, and solve for x (t).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e51c4f9-7707-4851-92b0-3f7eb5342ba2%2Fa3091a4e-3362-47cb-8bf9-be7156d8f763%2Fof937bs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Coupled
Harmonic
Oscillators
X2 :0
eeeee
Leeee NM
) Write down the 2nd law for each of the masses.
Use coordinates x, aud x, for m and M, and i,, *2 and a, a2.
Hirnt: the force from spring I on monly depends
on x, , but
the ferce from spring 2 on m
depand s
on (x2-x,)
two differantial
2) To simplify, let k, -k,k and m-M. Rewrite
egg equatious from i) right above each other.
your
3) Detine two new variables, X (Greek"chi") - x,+X2 and Ax = X,-x 2
two di ferential equations to produce
Then add and subtract
your
very simple (harmanic) ones.
4) Write down the solutiou to bothe equations using
Wask+2k2 ond evefficients A, B, C, and D
two new ,
but
w. :
un
5) Now assune k-10k2 (this means that the two masses are
"weakly coupled"). Also assume X,(0) = -10cm, x,(0)=0, xz (0)= o,
x,(0)=0. Solve for A,B, C, D, and solve for x (t).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
We will only answer the first question since the exact question to be answered was not specified. Please re-submit a new question specifying the one you'd like answered.
Step 2 (1)
Given, masses m and M. Where, M>m.
And, are the respective displacements of m and M from its equilibrium position.
We deduce,
So, writing Newton's second law of motion for both the masses.
For mass m:
For mass M:
Step by step
Solved in 3 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![College Physics](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
![University Physics (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
![Introduction To Quantum Mechanics](https://www.bartleby.com/isbn_cover_images/9781107189638/9781107189638_smallCoverImage.jpg)
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
![Physics for Scientists and Engineers](https://www.bartleby.com/isbn_cover_images/9781337553278/9781337553278_smallCoverImage.gif)
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
![Lecture- Tutorials for Introductory Astronomy](https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif)
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON