An engineer is interested in the horizontal displacement of the dynamic system depicted in Fig. Q1. The two solids have the same mass m, are connected by a spring with stiffness k, and are both connected to the ground by dampers (viscous damping) with a damping coefficient c. The horizontal displacement of the left mass is denoted by x₁ (t) and the horizontal displacement of the right mass is denoted by x2(t). Both masses are initially at rest (the initial displacement and speed are zero). A force f₁ (t) is applied on the left mass and a force f2(t) is applied on the right mass. Data: m = 2 kg. k = 1 N/m. c = 4 Ns/m. fi(t) = -1 N. f2(t) = 2 N. a) Show that the displacements x₁ (t) and x2 (t) are given by the solutions of the equations mä₁ (t) + cx₁ (t) + k(x₁(t) − x₂(t)) = f₁(t), mä₂(t)+ci₂(t) + k(x₂(t) = x₁(t)) = f₂(t). b) Introducing the change of variable 9₁ (t) = x₁(t) + x₂(t), 92 (t) = x₁(t) = x₂(t), and combining the two equations established in Q1-a, show that q₁ (t) and 92 (t) are given by the solutions of the equations 91 mäi(t) + cġ₁ (t) = f₁(t) + f₂(t), mä2 (t) + cġ₂ (t) + 2kq2 (t) = f₁(t) - f2(t). c) Calculate q₁ (t) and q2 (t) (hint for q₁ (t): introduce the change of variable z(t) = ġ₁ (t)) 91 d) Using 91 (t) and q2 (t) calculated in Q1-c and equations (1.3) and (1.4), calculate x₁ (t) and x₂(t).
An engineer is interested in the horizontal displacement of the dynamic system depicted in Fig. Q1. The two solids have the same mass m, are connected by a spring with stiffness k, and are both connected to the ground by dampers (viscous damping) with a damping coefficient c. The horizontal displacement of the left mass is denoted by x₁ (t) and the horizontal displacement of the right mass is denoted by x2(t). Both masses are initially at rest (the initial displacement and speed are zero). A force f₁ (t) is applied on the left mass and a force f2(t) is applied on the right mass. Data: m = 2 kg. k = 1 N/m. c = 4 Ns/m. fi(t) = -1 N. f2(t) = 2 N. a) Show that the displacements x₁ (t) and x2 (t) are given by the solutions of the equations mä₁ (t) + cx₁ (t) + k(x₁(t) − x₂(t)) = f₁(t), mä₂(t)+ci₂(t) + k(x₂(t) = x₁(t)) = f₂(t). b) Introducing the change of variable 9₁ (t) = x₁(t) + x₂(t), 92 (t) = x₁(t) = x₂(t), and combining the two equations established in Q1-a, show that q₁ (t) and 92 (t) are given by the solutions of the equations 91 mäi(t) + cġ₁ (t) = f₁(t) + f₂(t), mä2 (t) + cġ₂ (t) + 2kq2 (t) = f₁(t) - f2(t). c) Calculate q₁ (t) and q2 (t) (hint for q₁ (t): introduce the change of variable z(t) = ġ₁ (t)) 91 d) Using 91 (t) and q2 (t) calculated in Q1-c and equations (1.3) and (1.4), calculate x₁ (t) and x₂(t).
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
I am struggling with a, b,c,d
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 7 steps with 1 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