Consider the mechanical system in Figure 1. Assume the system is in equilibrium. Let the states be defined as: • z(t) = Fr, (t) - The force on spring k. • r2(t) = in (t) - The velocity of Mq. • zs(t) = Fk, (t) - The force on spring ką. • z(t) = 2(t): The velocity of M,. Ma Figure 1: Mechanical system The forces fi and f2 are the inputs to the system and the velocities ý, and ý2, the outputs. Determine the following state space model for the system in terms of the masses, damping coefficients, spring constants and forces shown in Figure 1: x(t) = Ax(t) +Bu(t) vít) - Cx(t) Du(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
icon
Related questions
Question
Consider the mechanical system in Figure 1. Assume the system is in equilibrium. Let the states be defined as:
1(t) = Fk, (t) - The force on spring k1.
12(t) = ÿ1 (t) - The velocity of M1.
• z3(t) = Fi(t) - The force on spring k2.
• za(t) = ý2(t): The velocity of M2.
M1
M2
Figure 1: Mechanical system
The forces fi and f2 are the inputs to the system and the velocities ý, and y2, the outputs. Determine the following
state space model for the system in terms of the masses, damping coefficients, spring constants and forces shown
in Figure 1:
x(t) = Ax(t) + Bu(t)
%3D
y(t) = Cx(t) + Du(t)
%3D
Transcribed Image Text:Consider the mechanical system in Figure 1. Assume the system is in equilibrium. Let the states be defined as: 1(t) = Fk, (t) - The force on spring k1. 12(t) = ÿ1 (t) - The velocity of M1. • z3(t) = Fi(t) - The force on spring k2. • za(t) = ý2(t): The velocity of M2. M1 M2 Figure 1: Mechanical system The forces fi and f2 are the inputs to the system and the velocities ý, and y2, the outputs. Determine the following state space model for the system in terms of the masses, damping coefficients, spring constants and forces shown in Figure 1: x(t) = Ax(t) + Bu(t) %3D y(t) = Cx(t) + Du(t) %3D
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY