Derive the state-space model (state equation and output equation) in vector form for thefollowing system. The system outputs are the displacements of each spring. Assume that theconnection between the spring and rope is massless and that the rope is inextensible. Assumethat gravity is an input as well as the applied forces Fi(t) and F2(t). Neglect friction forceson mass m₂.If q₁ is the state variable for the bottom spring connected to m₁, q2 is the state variable for themass m₁, q3 is the the top spring connected to the pulley, and q4 is the state variable connectedto the mass m2, then you should expect to get the following state-space representation:9243y0LaLa(L+L)04₂kL₂mi Li0m2013(L+L)0CA=- [8]9293 +9293 +L94m₂F₂(t)m₂TOLF₂(t)Figure 2: Diagram for problem 2X500X2[000]00U₁U12U13m₂.21142143

Given: To find: State-space model

Derive the state-space model (state equation and output equation) in vector form for the following system. The system outputs are the displacements of each spring. Assume that the connection between the spring and rope is massless and that the rope is inextensible. Assume that gravity is an input as well as the applied forces Fi(t) and F2(t). Neglect friction forces on mass m₂. If qi is the state variable for the bottom spring connected to m₁, q2 is the state variable for the mass m₁, q3 is the the top spring connected to the pulley, and q4 is the state variable connected to the mass m2, then you should expect to get the following state-space representation:

Derive the state-space model (state equation and output equation) in vector form for the following system. The system outputs are the displacements of each spring. Assume that the connection between the spring and rope is massless and that the rope is inextensible. Assume that gravity is an input as well as the applied forces Fi(t) and F2(t). Neglect friction forces on mass m₂. If qi is the state variable for the bottom spring connected to m₁, q2 is the state variable for the mass m₁, q3 is the the top spring connected to the pulley, and q4 is the state variable connected to the mass m2, then you should expect to get the following state-space representation:

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

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Concept explainers

Entropy

In physics, entropy means the amount of disorder or the degree of randomness associated with a thermodynamic system. The system is not self-organized when the entropy of the system is high. For instance, when a system is at an elevated temperature, its molecules are in random motion, vibrating and colliding with each other. During this scenario, the probability of finding a molecule at a particular place twice, is low. Under this circumstance, the system can be said to be in a high entropy.

Question

Derive the state-space model (state equation and output equation) in vector form for the
following system. The system outputs are the displacements of each spring. Assume that the
connection between the spring and rope is massless and that the rope is inextensible. Assume
that gravity is an input as well as the applied forces Fi(t) and F2(t). Neglect friction forces
on mass m₂.
If q₁ is the state variable for the bottom spring connected to m₁, q2 is the state variable for the
mass m₁, q3 is the the top spring connected to the pulley, and q4 is the state variable connected
to the mass m2, then you should expect to get the following state-space representation:
92
43
y
0
LaLa
(L+L)
0
4₂
kL₂
mi Li
0
m2
0
13
(L+L)
0
CA
=
- [8]
92
93 +
92
93 +
L94
m₂
F₂(t)
m₂
TOL
F₂(t)
Figure 2: Diagram for problem 2
X5
00
X2
[000]
00
U₁
U12
U13
m₂.
21
142
143

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