Sultan Qaboos University
College of Engineering
Department of Mechanical & Industrial Engineering
MEIE4122 ENGINEERING SYSTEMS AND CONTROL
Due
9th
of Oct 2022
Problem 1.
Two identical cylinders, each of radius r and mass m, are connected by a spring with
constant k and roll without slip relative to ground.
(a) Using Lagrange formulation derive the equation of motion of the system,
(b) Write the equations in state space form
x1
x2
k
r
m
The mass moment of
inertia about the mass
center of each cylinder is
J  12 mr 2 .
r
m
k
Problem 2.
Linear
dissipator,
b
For the spring pendulum system shown,
Derive the equations using Lagrange formulation
q1
a
q2
Problem 3.
A rigid, massless rod of length 2L is free to
rotate about a pivot through its center. Both ends of the rod
are attached to two identical, massless springs with spring
constant k. The other ends of the springs are fixed to the
ground. Initially, the rod is horizontal and both the springs
mg
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are un-stretched. A disc of mass m, radius r, and moment of inertia J is placed at the center of the
rod. The disc rolls on the rod without slippage. (The dashed lines in the figure show a possible
alternative configuration of the system)
Choose appropriate generalized coordinate(s) for this system and derive the equation(s) of motion
m, r , J
L
g
L
k
k
Problem 4.
for the following system
dy1
 y2
dt
dy 2
  1  y12 y 2  y1
dt
Where,   1
(a) Compute the stationary points
(b) Linearize around the stationary points
(c) Simulate the system using MATLAB from t=0 to t=20 sec, with y1(0)=y2=(0)=1;
(d) Plot y1 versus t and y2 versus t
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