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ME 218 (17795)
Alan ShuMing Kwok (sk25784)
Problem 1
1a). Use Matlab’s plotting function to identify the number of intersections these two functions have (plot
and identify by eye how many there are and roughly where they are)
clear
all
;
x = 8 : 0.05 : 8;
y1 = 3.*x.^3  4.*x + 7;
y2 = 19.*x.^2  30;
plot(x,y1,
'b'
,x, y2,
'r'
);
title(
'Problem 1  Find Intersections'
);
text(6,1000,
'19x^2  y  30 = 0'
);
text(6,1000,
'3x^3  4x  y + 7 = 0'
);
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View Full Document ME 218 (17795)
Alan ShuMing Kwok (sk25784)
Eyeapproximation: two intersections around (1.5,0) , (1.5,0) and (6.5, 700)
1b). Write a MATLAB function that takes an initial guess as an input and uses the vectorial Newton
Raphson’s method to find an intersection of these curves.
function
Ans = NR(x,y)
%Jacobian Matrix
Ja = 9*x^24;
Jb = 1;
Jc = 38*x;
Jd = 1;
ME 218 (17795)
Alan ShuMing Kwok (sk25784)
J = [ Ja Jb ; Jc Jd ];
f = 3*x^3  4*x y + 7;
g = 19*x^2  y  30;
%NR method
Ans = [ x; y ]  (J^1)*[ f; g];
%recursion NR iterations until results fall 0.001 within previous result
if
( abs(Ans  [x;y]) >= [0.001;0.001])
Ans = NR(Ans(1,1),Ans(2,1));
end
end
1c). Use your program to find all intersections of these two curves. Hint: select an initial guess near each
zero and start the procedure from that point. For your own records, keep tracking the progress of your
iterations to make sure that you are converging to the correct intersection and then report iterations for the
procedure that successfully converged to each of your intersections
>> NR(1.5,0)
Ans =
1.3652
5.0657
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Alan ShuMing Kwok (sk25784)
Ans =
1.3562
4.9429
ans =
1.3561
4.9424
>> NR(1.5,0)
Ans =
1.4601
10.4770
ans =
1.4599
10.4949
>> NR(6.5,700)
Ans =
6.2515
711.3583
Ans =
6.2297
707.3698
ans =
6.2296
707.3404
Problem 2
2b) If the pendulum is released from rest at the position given above, use the results of ODE45() to plot
the location of each joint for the 2 seconds after release. Create a second graph for a time span of 10
seconds. Both graphs should contain two plots in a single figure, which can be obtained using the subplot
command. All plots should be in degrees.
function
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This note was uploaded on 09/04/2011 for the course ME 218 taught by Professor Unknown during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Unknown

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