MEEN 364
Homework Set 4
Fall 2004
September 23, 2004
Homework Set 4 – Due September 30, 2004 @ 5:00 PM
1.
In the following problem, assume negligible thicknesses, massless bodies and frictionless
motion unless otherwise is stated. For the system shown below:
(a)
Derive the governing equations of motion.
(b)
Let
x
(
t
),
y
(
t
) and their first time derivatives be the state variables,
F
(
t
)
,
the input, and
y
(
t
), the output. Represent the equations you got in (a) in statespace representation.
There is no friction between the bodies.
x
(
t
)
y
(
t
)
2.
(a) Determine the governing equations of motion for the system given below. The
displacement of the mass and the disk are considered from the static equilibrium position
(SEP). The disk is fixed at its center and can freely rotate about it. Since the pulley
surrounded by the belt has a high friction, therefore, there is no slip.
(b)
Simulate the above system in MATLAB or Simulink and plot the displacement,
velocity of the block, angular displacement, and angular velocity of the disk with respect
to time.
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