Introduction to Matlab 6 for Engineers by ... T1.1-1 a) 6*10/13 + 18/(5*7) + 5*9^2.
... 6. 7. Time t (sec). Speed s (ft/sec). Figure : for Problem T1.3-5. T1.3-6 The ...
c Instructor’s Manual to accompany Introduction to Matlab 6 for Engineers by William J. Palm III University of Rhode Island
c Instructor’s Manual Copyright 2000 by McGraw-Hill Companies, Inc.
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Solutions to Problems in Chapter One Test Your Understanding Problems T1.1-1 a) 6*10/13 + 18/(5*7) + 5*9^2. Answer is 410.1297. b) 6*35^(1/4) + 14^0.35. Answer is 17.1123. T1.3-1 The session is: x = [[cos(0):0.02:log10(100)]; length(x) ans = 51 x(25) ans = 1.4800
T1.3-2 The session is: roots([1, 6, -11, 290] ans = -10.000 2.0000 + 5.0000i 2.0000 - 5.0000i poly(ans) ans = 1.0000 6.0000 -11.0000 290.0000 which are the given coefficients. Thus the roots are −10 and 2 ± 5i. T1.3-3 a) b) z = c) z = d) z =
z 1 1 0
= 0 0 0
0 0 1 0
0 0 1 0
1 1 1 0 1 1
T1.3-4 The session is: x = [-4, -1, 0, 2, 10];y = [-5, -2, 2, 5, 9]; x(x>y) ans = -4 -1 10 find(x>y) ans = 1 2 5
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T1.3-5 The session is: t = [0:0.01:5]; s = 2*sin(3*t+2) + sqrt(5*t+1); plot(t,s),xlabel(0Time (sec)0 ),ylabel(0Speed (ft/sec)0)
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Speed s (ft/sec)
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1
0
0
0.5
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1.5
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2.5 Time t (sec)
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Figure : for Problem T1.3-5 T1.3-6 The session is: x = [0:0.01:1.55]; s = 4*sqrt(6*x+1); z = polyval([4,6,-5,3],x); plot(x,y,x,z,0--0 ),xlabel(0Distance (meters)0),ylabel(0Force (newtons)0
T1.3-7 The session is: A = [6, -4, 8; -5, -3, 7; 14, 9, -5]; b = [112; 75; -67]; x = A\b 1-2
25
Force (newtons)
20
15
10 y
5 z
0
0
0.5
1 Distance x (meters)
Figure : for Problem T1.3-6 x = 2.0000 -5.0000 10.0000 A*x ans = 112 75 -67 Thus the solution is x = 2, y = −5, and z = 10. T1.4-1 The session is: a = 112; b = 75; c = -67; A = [6, -4, 8; -5, -3, 7; 14, 9, -5]; bvector = [a; b; c]; x = A\bvector x = 2.0000 -5.0000 10.0000 1-3
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A*x ans = 112 75 -67 Thus the solution is x = 2, y = −5, and z = 10. T1.4-2 The script file is: x = -5; if x < 0 y = sqrt(x^2+1) elseif x < 10 y = 3*x+1 else y = 9*sin(5*x-50)+31 end For x = −5, y = 5.0990. Changing the first line to x = 5 gives y = 16. Changing the first line to x = 15 gives y = 29.8088. T1.4-3 The script file is sum = 0; for k = 1:20 sum = sum + 3*k^2; end sum The answer is sum = 8610. T1.4-4 The script file is sum = 0;k = 0; while sum y) ans = -15 9 find(x>y) ans = 1 3 The first and third elements of x are greater than the first and third elements of y. 20. The session is: t = [1:0.005:3]; T = 6*log(t) - 7*exp(-0.2*t); plot(t,T),title(0Temperature Versus Time0 ),... xlabel(0Time t (minutes)0),ylabel(0Temperature T (◦ C)0 ) The plot is shown in the figure. 1-10
Temperature Versus Time 3
2
1
o
Temperature T ( C)
0
−1
−2
−3
−4
−5
−6
1
1.2
1.4
1.6
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2 2.2 Time t (minutes)
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Figure : for Problem 20 21. The session is: x = [0:0.01:2]; u = 2*log10(60*x+1); v = 3*cos(6*x); plot(x,u,x,v,0--0 ),ylabel(0Speed (miles/hour)0),... xlabel(0Distance x (miles)0) The plot is shown in the figure.
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5
4 u
Speed (miles/hour)
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v
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1
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0.8 1 1.2 Distance x (miles)
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Figure : for Problem 21
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1.6
1.8
2
22. The session is: x = [-3:0.01:3]; p1 = [3,-6,8,4,90]; p2 = [3,5,-8,70]; y = polyval(p1,x); z = polyval(p2,x); plot(x,y,x,z,0--0 ),ylabel(0Current (milliamps)0),... xlabel(0Voltage x (volts)0 ) The plot is shown in the figure. 600
500
Current (milliamps)
400
300
y
200
100 z
0 −3
−2
−1
0 Voltage x (volts)
1
Figure : for Problem 22
1-13
2
3
23. The session is: p = [3,-5,-28,-5,200]; x = [-1:0.005:1]; y = polyval(p,x); plot(x,y),ylabel(0y0 ),xlabel(0x0 ),ginput(1) The peak as measured with the mouse cursor is y = 200.3812 at x = −0.0831 205
200
y
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175 −1
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0 x
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Figure : for Problem 23 24. The session is: A = [7,14,-6;12,-5,9;-5,7,15]; b = [95;-50;145]; x = A\b The answers are −3, 10, and 4, which correspond to x = −3, y = 10, and z = 4. Typing A*x gives the result 95, -50, 145, which are the right-hand sides of the equations. Thus the values of x, y, and z are correct. 25. The script file is: 1-14
x = -5; if x < -1 y = exp(x + 1) elseif x < 5 y = 2 + cos(pi*x) else y = 10*(x - 5) + 1 end The answer for x = −5 is y = 0.0183. Change the first line to x = 3 to obtain y = 1. Then change the first line to x = 15 to obtain y = 101. 26. The script file is: sum = 0; for k = 1:10 sum = sum + 5*k^3; end sum The answer is sum = 15125. 27. The script file is: sum = 0;k = 0; while sum
