Chapter5

Problem 1

Script file:

%problem 1 Use the plot command to plot the function

%when x is less than or equal to 5, and greater than or equal to 0.

%type [0 5]page 141

figure(1)

fplot(@ (x) x.^2-10.*sqrt(x)+2,[0 5])

Problem 2

Script file:

%problem 2

figure(2)

x = -3:0.01:10;

y = (0.5*x.^4 + 1.1*(x.^3)-0.9*(x.^2)).*exp(-0.7*x);

plot(x,y)

Problem 3

Script file:

%problem 3

figure(3)

fplot(@ (x) 3.*cos(1.7*x).*exp(-0.3*x)+2.*sin(1.4*x).*exp(0.3*x),[-7 7])

Problem 4

Script file:

%problem 4

figure(4)

x=[0:0.01:10];

y=x.^2.*exp(-x);

yd=2.*x.*exp(-x)-exp(-x).*x.^2;

plot(x,y,’-‘, x,yd,’–‘)

Problem 5

Script file:

%problem 5

figure(5)

x1=[-3:0.01:4];

x2=[0:0.01:1];

y1= x1.^4-2.*x1.^3+1.3.*x1.^2-0.3.*x1+0.02;

y2= x2.^4-2.*x2.^3+1.3.*x2.^2-0.3.*x2+0.02;

plot(x1,y1)

plot(x2,y2)

Problem 6

Script file:

%problem 6

figure(6)

fplot(@ (x) 5*(exp(-0.5*x)-exp(-0.8*x)),[0 10])

Problem 7

Script file:

%problem 7

figure(7)

x = -pi:0.01:2*pi;

y = sin(2*x).*(cos(0.5*x)).^2;

yd = ((2.*(cos((0.5).*x).^2).*cos(2.*x))-(0.5.*sin(x).*sin(2.*x)));

plot(x,y,’-‘,x,yd,’–‘);

Problem 8

Script file:

%problem 8

figure(8)

th=linspace(0,2*pi,200);

r=3.44e7./(1-0.206*cos(th));

polar(th,r)

Problem 9

Script file:

%problem 9

figure(9)

t = [0:0.01:2*pi];

x = 0.7*sin(10*t);

y = 1.2*sin(8*t);

plot(x,y);

axis([-1.5, 1.5, -1.5, 1.5]);

Problem 10

Script file:

%problem 10

figure(10)

t = [0:0.01:2*pi];

x = sin(t).*((exp(cos(t))-(2.*cos(4.*t))+((sin(t./12)).^5)));

y = cos(t).*((exp(cos(t))-(2.*cos(4.*t))+((sin(t./12)).^5)));

subplot(2,1,1);

plot(x,y)

t = [0:0.01:10*pi];

x = sin(t).*((exp(cos(t))-(2.*cos(4.*t))+((sin(t./12)).^5)));

y = cos(t).*((exp(cos(t))-(2.*cos(4.*t))+((sin(t./12)).^5)));

subplot(2,1,2)

plot(x,y)

Problem 11

Script file:

%problem 11

figure(11)

x = 0: 0.01 : 1;

y = (1-x.^(2/3)).^(3/2);

yn = -y;

xn = 0: -0.01: -1;

plot(x,y,’k’,x,yn,’k’,xn,y,’k’,xn,yn,’k’)

axis square

Problem 12

Script file:

%problem 12

figure (12)

xi = -pi:0.01:pi;

x = (cos(xi)).^3;

y = (sin(xi)).^3;

plot(x,y);

axis([-1.5, 1.5, -1.5, 1.5]);

Problem 13

Script file:

%problem 13

figure (13)

x1=0:0.01:1.9;

x2=2.1:0.01:4;

y1= (x1.^2-6*x1+7)./(x1.^3-8);

y2= (x2.^2-6*x2+7)./(x2.^3-8);

plot(x1, y1, x2, y2)

Problem 14

Script file:

%problem 14

figure(14)

x1=[-4:0.005:-1.01];

x2=[-0.99:0.005:0.99];

x3=[1.01:0.005:4];

y1=x1+(1./(x1.^2-1));

y2=x2+(1./(x2.^2-1));

y3=x3+(1./(x3.^2-1));

plot(x1, y1, ‘k’, x2, y2, ‘k’, x3, y3, ‘k’);

axis([-4, 4, -15, 15]);

Problem 15

Script file:

%problem 15

figure(15)

x=linspace(-1,1,200);

ya=(x.^2).^(1/3)+ sqrt(1-x.^2);

yb=(x.^2).^(1/3)- sqrt(1-x.^2);

plot(x, ya, ‘k’, x, yb, ‘k’);

axis equal

Problem 16

Script file:

%problem 16

figure(16)

t=[-4:0.005:4];

x= (3.3-0.3*t.^2).*(cos(t));

y=(3.3-0.4*t.^2).*(sin(t));

plot(x,y, ‘k’, ‘LineWidth’, 35)

axis([-2,4,-3,3])

Problem 17

Script file:

%problem 17

figure(17)

th=linspace(0,5*pi,200);

r=th.^0.5;

polar(th, r, ‘k’)

hold on

polar(th, -r, ‘k’)

hold off

Problem 18

Script file:

%problem 18

figure(18)

n=1:100;

th=135.7*n*pi/180;

r=1*n.^0.5;

polar(th, r,’o’)

Problem 19

Script file:

%problem 19

figure(19)

t=(-.75:.01:2.25);

r=(sin(2.*t))./(((cos(t)).^3)+((sin(t)).^3));

x=r.*cos(t);

y=r.*sin(t);

plot(x,y,’k’)

axis([-2,2,-2,2])

Problem 20

Script file:

%problem 20

figure(20)

% ((x^2)/(a^2))+((y^2)/(b^2))=1

a=10;

b=4;

x=[-10:.01:10];

theta=30;

y1=sqrt((1-((x.^2)/(a^2))).*(b^2));

y2=-sqrt((1-((x.^2)/(a^2))).*(b^2));

% The rotated ellipse

x3=(x.*cosd(theta))+(y1.*sind(theta));

y3=-((-x.*sind(theta))+(y1.*cosd(theta)));

y4=-y3;

plot(x,y1,’r’,x,y2,’r’,x3,y3,’–b’,-x3,y4,’–b’)

axis([-15,15,-10,10])

Problem 21

Script file:

%Problem 21

figure(21)

t=[10:10:70];

H1=[9 22 44 63 80 94 97];

H2=(100.8)./(1+(23.*(exp(-0.093.*t))));

plot(t,H1,’o’,t,H2,’r’)

legend(‘Height Data’,’Height Calculated’,’Time’)

xlabel(‘Time’)

ylabel(‘Height’)

Problem 22

Script file:

% Problem 22

figure(22)

t=[0:.01:15];

vc=36.*(1-exp(-t./3));

plot(t,vc)

grid on

xlabel(‘Time’)

ylabel(‘Voltage’)

Problem 23

Script file:

% Problem 23

figure(23)

E0=0.885e-12;

q=2.4e-5;

Q=9.4e-6;

R=.1;

z=[0:.01:.3];

F=((Q.*q.*z)/(2.*E0)).*(1-(z./(sqrt((z.^2)+(R.^2)))));

plot(z,F,’b’);

[A B]=max(F);

fprintf(‘The Maximum of F is %3.2f and the Corresponding Z is %3.2f\n’,A,z(B))

Problem 24

Script file:

% Problem 24

figure(24)

t=[0:.1:5];

x=(52.*t)-(9.*(t.^2));

y=(125-(5.*(t.^2)));

vx=52-(18.*t);

vy=-10.*t;

v=sqrt((vx.^2)+(vy.^2));

[A B]=min(v);

subplot(2,1,1)

plot(x,y,’b’,x(B),y(B),’*’)

xlabel(‘X-Position’)

ylabel(‘Y-Position’)

subplot(2,1,2)

plot(t,v,’k’)

xlabel(‘Time’)

ylabel(‘Velocity’)

fprintf(‘The minimum Velocity is %4.2f and the position of the particle at that time is (%4.2f,%4.2f)\n’,A,x(B),y(B))

Problem 25

Script file:

% Problem 25

figure(25)

t=[0:.01:38.32];

g=9.81;

V0=200;

theta=70;

h=( V0 .* t .* sind(theta) )-( ( g .* (t.^2) ) ./2 );

v=sqrt((V0.^2)-(2.*V0.*g.*t.*(sind(theta)))+((g.^2).*(t.^2)));

tmin=2*(V0.*sind(theta))./g;

Vmin=min(tmin);

subplot(2,1,1)

plot(t,h,’-b’)

xlabel(‘Time’)

ylabel(‘Height’)

legend(‘Time vs Height’)

subplot(2,1,2)

plot(t,v,’-r’)

xlabel(‘Time’)

ylabel(‘Velocity’)

legend(‘Time Vs Velocity’)

fprintf(‘The time it will take for the projectile to hit the ground is %5.2f seconds\n’,Vmin)

Problem 26

Script file:

% Problem 26

figure(26)

t=[0:.01:8];

pt=(8-(4.*(t.^3).*exp(-0.4.*t))+(2.*(t.^2)));

x=(8-(4.*(t.^3).*exp(-0.4.*t))+(2.*(t.^2)));

vt=t.*(exp(-0.4.*t).*t.*(1.6.*t-12)+4);

at=(4.29005.*(t.^3))-(24.1315.*(t.^2))+4;

subplot(3,1,1)

plot(t,x,’r’)

xlabel(‘Time’)

ylabel(‘Position’)

subplot(3,1,2)

plot(t,vt,’b’)

xlabel(‘Time’)

ylabel(‘Velocity’)

subplot(3,1,3)

plot(t,at,’g’)

xlabel(‘Time’)

ylabel(‘Acceleration’)

Problem 27

Script file:

%problem 27

figure(27)

c=3.*10.^8;

h=6.626.*10.^-34;

k=1.38.*10.^-23;

Lambda=[ 0.1 : .001 : 3 ];

lambda=Lambda.*1e-6;

T=[3000 4000 5000];

R1= (2*pi.*h.*(c.^2))./((lambda.^5).*(exp((h.*c)./(k.*T(1).*lambda))-1));

R2= (2*pi.*h.*(c.^2))./((lambda.^5).*(exp((h.*c)./(k.*T(2).*lambda))-1));

R3= (2*pi.*h.*(c.^2))./((lambda.^5).*(exp((h.*c)./(k.*T(3).*lambda))-1));

plot(lambda,R1,’-r’,lambda,R2,‘-g’,lambda,R3,’-k’)

legend(‘T=3000k’,’T=4000k’,’T=5000k’)

xlabel(‘Wavelength (microm)’)

ylabel(‘Spectral Energy Density (W/m^3)’)

Problem 28

Script file:

%problem 28

figure(28)

f=[10:1:50000];

w=2.*pi.*f;

R=2000;

C=0.2e-6;

v0v1=(w.*R.*C)./((1+(w.^2).*(R.^2).*(C.^2)).^(1/2));

semilogx(f,v0v1,’r’)

xlabel(‘Frequency (Hz)’)

ylabel(‘V0/Vi’)

Problem 29

Script file:

%problem 29

figure(29)

R=4;

L=1.3;

V=12;

t1=[0:.01:.5];

it1=(V./R).*(1-exp((-R.*t1)./(L)));

t2=[.5:.01:2];

it2=(exp(-(R.*t2)./L)).*(V./R).*(exp(0.5.*R./L)-1);

plot(t1,it1,’k’,t2,it2,’k’)

xlabel(‘Time’)

ylabel(‘Current’)

Problem 30

Script file:

%problem 30

figure(30)

F = [0 4390 7250 10780 11710 12520 12800 13340 13740 13820 13850 13910 13990 14020 14130];

L=[0.5 .50146 .50226 .50344 .50423 .50577 .50693 .51138 .52006 .52169 .52362 .52614 .53406 .54018 .56466];

r = 0.25;

A0 = 0.5;

L0 = 0.5;

sigmae=(F)./(A0);

epsilone=(L-L0)./(L0);

sigmat=(F.*L)./(A0.*L0);

epsilont=log(L./L0);

subplot(2,1,1)

plot(F,sigmae,’c’,F,sigmat,’–b’)

xlabel(‘Force (lb)’)

ylabel(‘Length (in)’)

legend(‘Engineering Stress’,’True Stress’)

subplot(2,1,2)

plot(F,epsilone,’g’,F,epsilont,’–r’)

xlabel(‘Force (lb)’)

ylabel(‘Length (in)’)

legend(‘Engineering Strain’,’True Strain’)

Problem 31

Script file:

%problem 31

figure(31)

c=300e6;

L=2;

v=[0:100:300e6];

delta=L.*(1-(sqrt(1-((v.^2)./(c.^2)))));

plot(v,delta,’r’)

xlabel(‘Velocity’)

ylabel(‘Delta’)

semilogx(v,delta,’k’)

xlabel(‘Velocity’)

ylabel(‘Delta’)

loglog(v,delta,’b’)

xlabel(‘Velocity’)

ylabel(‘Delta’)

Problem 32

Script file:

%problem 32

figure(32)

t=[0:.01:4];

xt=4.219.*(exp(-1.58.*t)-exp(-6.32.*t));

vt=(26.67.*(exp(-6.32.*t)))-(6.67.*(exp(-1.58.*t)));

subplot(2,1,1)

plot(t,xt,’r’)

xlabel(‘Time’)

ylabel(‘Position’)

subplot(2,1,2)

plot(t,vt,’b’)

xlabel(‘Time’)

ylabel(‘Velocity’)

Problem 33

Script file:

%problem 33

figure(33)

R=0.08206;

a=3.592;

b=0.04267;

n=1;

T=297;

V=[0.065:.001:1];

PI=(n).*(R).*(T)./(V);

PVdW=((n.*R.*T)./(V-(n.*b)))-(((n.^2).*a)./(V.^2));

plot(V,PI,’–r’,V,PVdW,’b’)

title(‘Gas Isotherms’)

xlabel(‘Volume’)

ylabel(‘Pressure’)

legend(‘Ideal Gas Law’,’Van der Waals’)

Problem 34

Script file:

%problem 34

figure(34)

f1=130;

f2=120;

t=[0:.001:.3];

y1=cos(2.*pi.*f1.*t);

y2=cos(2.*pi.*f2.*t);

y=2.*cos(2.*pi.*((f1+f2)./2).*t).*cos(2.*pi.*((f1-f2)./2).*t);

plot(t,y,’k’)

xlabel(‘Time (s)’)

ylabel(‘Amplitude’)

Problem 35

Script file:

%problem 35

figure(35)

I0=10e-14;

vS=1.5;

R=1200;

ktq=0.030;

vD=[0:.01:1.5];

iD1=I0.*(exp((vD./ktq))-1);

iD2=(vS-vD)./R;

intersection = find(iD1-iD2<eps,1);

px=iD2(intersection);

py=iD2(intersection);

plot(vD,iD1,’r’,vD,iD2,’r’,px,py,’o’)

axis([0,1.5,-.02,0.02])

Problem 36

Script file:

%problem 36

figure(36)

lambda=4.80e-7;

a=0.025e-3;

d=0.09e-3;

L=100;

y=[-4:.01:4];

R=sqrt(L.^2+y.^2);

alpha=(pi.*a)./(lambda).*(y./R);

beta=(pi.*d)./(lambda).*(y./R);

I=(cos(beta).^2).*((sin(alpha)./alpha).^2);

plot(y,I,’k’)

xlabel(‘Distance (cm)’)

ylabel(‘Relative Intensity’)

Problem 37

Script file:

%problem 37

figure(37)

x1=[0:.01:8];

Vx1=400-200.*x1;

Mx1=-100.*(x1.^2)+400.*x1;

x2=[8:.01:12];

Vx2=-1200.*(x2./x2);

Mx2=-1200.*x2+6400;

x3=[12:.01:20];

Vx3=-250.*x3+5000;

Mx3=(-125.*((x3-12).^2))+(2000.*x3)-32000;

subplot(2,1,1)

plot(x1,Vx1,’r’,x2,Vx2,’r’,x3,Vx3,’r’)

legend(‘Shear Force’)

xlabel(‘Distance ft’)

ylabel(‘Shear Force’)

subplot(2,1,2)

plot(x1,Mx1,’b’,x2,Mx2,’b’,x3,Mx3,’b’)

legend(‘Bending Moment’)

xlabel(‘Distance ft’)

ylabel(‘Bending Moment’)

Problem 38

Script file:

%problem 38

figure(38)

Q=300;

D=[100:.01:2000];

L0=[5 10 20];

Lc1=(L0(1))./(1+(2.5.*(D.^(2/3)))./(sqrt(Q)));

Lc2=(L0(2))./(1+(2.5.*(D.^(2/3)))./(sqrt(Q)));

Lc3=(L0(3))./(1+(2.5.*(D.^(2/3)))./(sqrt(Q)));

subplot(3,1,1)

plot(D,Lc1,’r’)

xlabel(‘X Side’)

ylabel(‘Y Side’)

subplot(3,1,2)

plot(D,Lc2,’r’)

xlabel(‘X Side’)

ylabel(‘Y Side’)

subplot(3,1,3)

plot(D,Lc3,’r’)

xlabel(‘X Side’)

ylabel(‘Y Side’)

Problem 39

Script file:

%problem 39

figure(39)

t=0.12;

p=0.4;

m=0.04;

c=1.5;

x1=[0:.01:p.*c];

x2=[p.*c:.01:c];

yt1=5.*t.*c.*((0.2969).*sqrt(x1./c)-0.126.*(x1./c)-0.3516.*((x1./c).^2)+0.2843.*((x1./c).^3)-0.1015.*((x1./c).^4));

yt2=5.*t.*c.*((0.2969).*sqrt(x2./c)-0.126.*(x2./c)-0.3516.*((x2./c).^2)+0.2843.*((x2./c).^3)-0.1015.*((x2./c).^4));

theta1=atan((2.*m)./(p.^2).*(p-(x1./c)));

theta2=atan((2.*m)./((1-p.^2)).*(p-(x2./c)));

yc1=(m.*(x1./(p.^2)).*((2.*p)-(x1./c)));

yc2=(m.*(c-x2)./((1-p).^2).*(1+(x2./c)-2.*p));

xU1=x1-yt1.*sind(theta1);

xL1=x1+yt1.*sind(theta1);

xU2=x2-yt2.*sind(theta2);

xL2=x2+yt2.*sind(theta2);

yU1=yc1+(yt1.*(cosd(theta1)));

yL1=yc1-(yt1.*(cosd(theta1)));

yU2=yc2+(yt2.*(cosd(theta2)));

yL2=yc2-(yt2.*(cosd(theta2)));

plot(xU1,yU1,’k’,xU2,yU2,’k’,xL1,yL1,’k’,xL2,yL2,’k’)

axis([0,1.5,-.2,.2])

xlabel(‘x (m)’)

ylabel(‘y (m)’)

Problem 40

Script file:

%problem 40

figure(40)

x=[0:.01:4.5];

y=sin(x).^2;

y2=(x.^2)-(((2.^3).*(x.^4))./(4.*3.*2.*1));

y3=(x.^2)-(((2.^3).*(x.^4))./(4.*3.*2.*1))+(((2.^5).*(x.^6))./(6.*5.*4.3.*2.*1));

y5=(x.^2)-(((2.^3).*(x.^4))./(4.*3.*2.*1))+(((2.^5).*(x.^6))./(6.*5.*4.3.*2.*1))-(((2.^5).*(x.^6))./(6.*5.*4.3.*2.*1))+(((2.^7).*(x.^8))./(8.*7.*6.*5.*4.*3.*2.*1));

plot(x,y,’k’,x,y2,’–r’,x,y3,’–b’,x,y5,’–g’)

legend(‘Sin^2(x)’,’Two Terms’,’Three Terms’,’Five Terms’)

xlabel(‘X’)

ylabel(‘sin^2(x)’)

axis([-1,5,-.2,1.5])