ME 218: ENGINEERING COMPUTATIONAL METHODS
Home Work #5
Assigned: October 6, 2011
Due: October 13, 2011
Name: __________________UT EID: ____________Unique: _________
Lab Time: (Mon/Tue)
___PM
Problem 1:
Find an intersections of curves
!
!
+
!
!
=
9
(a circle)
!
!
−
!
=
2
(an exponential curve)
that is close to the point
(
0
,
−
1
)
. Use the vectorial Newton Raphson method starting from
the point
!
!
,
!
!
=
(
0
,
−
1
)
and perform 3 iterations of the method and do it using a
simple scientific calculator (use a computer to perhaps confirm your findings). Please
maintain 4 decimal digits throughout your calculations.
Problem 2: (basically, a variation of the example postulated in
class)
Velocity of a mass
m
falling with initial velocity zero through the air (gaseous fluid) with
the coefficient of linear friction
c
is described as a function of time by the following
equation (you will learn this in ME344):
v
(
t
)
=
mg
c
1
−
e
−
ct
m
#
$
%
'
(
Let us assume we know that the gravitational constant
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 Fall '08
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 Mass, Jacobian, Newton Raphson Method

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