PRACTICE PROBLEM 8.2 two minecarts are connected as shown below. Friction is negligible. Assume that x1 & x2 is the displacement of the mass of the first cart and the mass of the second cart from their starting positions respectively. KI Differential eq: E x" If you know that: Both minecarts have a mass = 2 kilograms Spring constant (kl)=72N/m Spring constant (k2)=108N/m Spring constant (k3)=72N/m = Make a second order differential equations system that models the situation and find the general solution to the system you make. x m₁ General solution: [x₁(t) [x₂( M₂ = [](²₁ co [-] K3 (a₁ cos (-) + b₁ sin (-)) + [-] (a2 cos (-) + b₂ sin (−))
PRACTICE PROBLEM 8.2 two minecarts are connected as shown below. Friction is negligible. Assume that x1 & x2 is the displacement of the mass of the first cart and the mass of the second cart from their starting positions respectively. KI Differential eq: E x" If you know that: Both minecarts have a mass = 2 kilograms Spring constant (kl)=72N/m Spring constant (k2)=108N/m Spring constant (k3)=72N/m = Make a second order differential equations system that models the situation and find the general solution to the system you make. x m₁ General solution: [x₁(t) [x₂( M₂ = [](²₁ co [-] K3 (a₁ cos (-) + b₁ sin (-)) + [-] (a2 cos (-) + b₂ sin (−))
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![PRACTICE PROBLEM 8.2
two minecarts are connected as shown below. Friction
is negligible.
Assume that x1 & x2 is the displacement of the mass of
the first cart and the mass of the second cart from
their starting positions respectively.
KI
m,
www m₂
If you know that:
Both minecarts have a mass = 2 kilograms
Spring constant (kl)=72N/m
Spring constant (k2)=108N/m
Spring constant (k3)=72N/m
Differential eq:
ď = [ 3
x
K3
www
Make a second order differential equations system that
models the situation and find the general solution to
the system you make.
General solution:
[x₁(t)
[2²2(b)] = [-] (a₁ cos (-) + b₁ sin (-)) + [-] (0₂0
[x₂(t)
(a2 cos (-) + b₂ sin (-))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd61aa0cc-194b-4783-aa03-3c5c9cda5609%2F789b8f17-8578-4642-9f1f-a6b00024b057%2Fsdcqy2n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:PRACTICE PROBLEM 8.2
two minecarts are connected as shown below. Friction
is negligible.
Assume that x1 & x2 is the displacement of the mass of
the first cart and the mass of the second cart from
their starting positions respectively.
KI
m,
www m₂
If you know that:
Both minecarts have a mass = 2 kilograms
Spring constant (kl)=72N/m
Spring constant (k2)=108N/m
Spring constant (k3)=72N/m
Differential eq:
ď = [ 3
x
K3
www
Make a second order differential equations system that
models the situation and find the general solution to
the system you make.
General solution:
[x₁(t)
[2²2(b)] = [-] (a₁ cos (-) + b₁ sin (-)) + [-] (0₂0
[x₂(t)
(a2 cos (-) + b₂ sin (-))
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 20 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY