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ArhamQadeer

This document contains 23 solved problems involving MATLAB script files and plots. Each problem demonstrates a different mathematical or engineering concept, such as plotting functions, modeling circuits, or displaying particle velocity distributions. The scripts generate various graphs and plots to visualize solutions or relationships between variables.

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1 Chapter 5 Solved Problems Problem 1 Script File: x=linspace(-3,5,200); y=(x+5).^2./(4+3*x.^2); plot(x,y) xlabel('x') ylabel('y') -3 -2 -1 0 1 2 3 4 5 0 1 2 3 4 5 6 7 x y
2 Chapter 5: Solved Problems Problem 2 Script File: fplot('5*sin(x)/(x+exp(-0.75*x))',[-5 10]) xlabel('x') ylabel('y') -5 0 5 10 -4 -3 -2 -1 0 1 2 3 x y
Chapter 5: Solved Problems 3 Problem 3 Script file: x1=linspace(0,3,200); y1=(x1+1).*(x1-2).*(2*x1-0.25)-exp(x1); x2=linspace(-3,6,200); y2=(x2+1).*(x2-2).*(2*x2-0.25)-exp(x2); plot(x1,y1) xlabel('x') ylabel('y') figure plot(x2,y2) xlabel('x') ylabel('y') 0 0.5 1 1.5 2 2.5 3 -10 -8 -6 -4 -2 0 2 4 x y -3 -2 -1 0 1 2 3 4 5 6 -80 -60 -40 -20 0 20 40 x y
4 Chapter 5: Solved Problems Problem 4 Script File: plot('sqrt(abs(cos(3*x)))+sin(4*x)^2',[-2 2]) xlabel('x') ylabel('y')) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x y
Chapter 5: Solved Problems 5 Problem 5 Script File: fplot('exp(2*sin(0.4*x))*5*cos(4*x)',[-20 30]) xlabel('x') ylabel('y') -20 -15 -10 -5 0 5 10 15 20 25 30 -40 -30 -20 -10 0 10 20 30 40 x y
6 Chapter 5: Solved Problems Problem 6 Script File: t=linspace(0,2*pi,100); x=1.5*sin(5*t); y=1.5*cos(3*t); plot(x,y) axis([-2 2 -2 2]) xlabel('x') ylabel('y') -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x y
Chapter 5: Solved Problems 7 Problem 7 x1=-4:0.05:-1.1; x2=-0.9:0.05:3; y1=(x1.^2+3*x1+3)./(0.8*(x1+1)); y2=(x2.^2+3*x2+3)./(0.8*(x2+1)); plot(x1,y1,x2,y2) xlabel('x') ylabel('y') -4 -3 -2 -1 0 1 2 3 -15 -10 -5 0 5 10 15 x y
8 Chapter 5: Solved Problems Problem 8 t1=linspace(-30,-1.6,500); t2=linspace(-0.6,40,500); x1=3*t1./(1+t1.^3); y1=3*t1.^2./(1+t1.^3); x2=3*t2./(1+t2.^3); y2=3*t2.^2./(1+t2.^3); plot(x1,y1,x2,y2) xlabel('x') ylabel('y') -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x y
Chapter 5: Solved Problems 9 Problem 9 x1=-6:0.05:-2.1; x2=-1.9:0.05:2.8; x3=3.2:0.05:6; y1=(x1.^2-4*x1-7)./(x1.^2-x1-6); y2=(x2.^2-4*x2-7)./(x2.^2-x2-6); y3=(x3.^2-4*x3-7)./(x3.^2-x3-6); plot(x1,y1,x2,y2,x3,y3) %axis([-10 10 -30 30]) xlabel('x') ylabel('y') -6 -4 -2 0 2 4 6 -10 -5 0 5 10 15 x y
10 Chapter 5: Solved Problems Problem 10 r=1.5; t=linspace(0,4*pi,300); x=r*(t-sin(t)); y=r*(1-cos(t)); plot(x,y) xlabel('x') ylabel('y') 0 2 4 6 8 10 12 14 16 18 20 0 0.5 1 1.5 2 2.5 3 x y
Chapter 5: Solved Problems 11 Problem 11 x=linspace(-pi,pi,200); f=cos(x).*sin(2*x); df=2*cos(2*x).*cos(x)-sin(2*x).*sin(x); plot(x,f,x,df,'--') xlabel('x') ylabel('f(x), df(x)/dx') legend('f(x)','df(x)/dx') -4 -3 -2 -1 0 1 2 3 4 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x f(x), df(x)/dx f(x) df(x)/dx
12 Chapter 5: Solved Problems Problem 12 Command Window: >> fplot('693.8-68.8*cosh(x/99.7)',[-300 300]) -300 -200 -100 0 100 200 300 -100 0 100 200 300 400 500 600 700
Chapter 5: Solved Problems 13 Problem 13 Script File: vs=12; rs=2.5; RL=1:0.05:10; P=vs^2*RL./(RL+rs).^2; plot(RL,P) xlabel('R_L (Omega)') ylabel('P (W)') 1 2 3 4 5 6 7 8 9 10 9 10 11 12 13 14 15 RL (Ω) P (W)
14 Chapter 5: Solved Problems Problem 14 Script File: t=0:0.01:4; tDay=8+t; vA=27; vB=14; xA=-36+vA*cosd(30)*t; yA=12-vA*sind(30)*t; xB=-18+vB*cosd(70)*t; yB=-45+vB*sind(70)*t; dis=sqrt((xB-xA).^2+(yB-yA).^2); plot(tDay,dis) xlabel('Time of the Day') ylabel('Distance Between the Ships (mi)') 8 8.5 9 9.5 10 10.5 11 11.5 12 10 20 30 40 50 60 70 80 Time of the Day Distance Between the Ships (mi)
Chapter 5: Solved Problems 15 Problem 15 Kab=1.6; Kel=0.45; C=140; t=0:0.05:10; Cp=C*Kab/(Kab-Kel)*(exp(-Kel*t)-exp(-Kab*t)); plot(t,Cp) xlabel('t (h)') ylabel('Cp (mg/L)') 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 70 80 90 t (h) Cp (mg/L)
16 Chapter 5: Solved Problems Problem 16 Script File: t=0:0.1:20; r= 20+ 30*(1-exp(-0.1*t)); th=pi*(1-exp(-0.2*t)); x=r.*cos(th); y=r.*sin(th); thdot=pi*0.2*exp(-0.2*t); v=r.*thdot; plot(x,y) axis equal xlabel('x (m)') ylabel('y (m)') figure plot(t,v) xlabel('t (s)') ylabel('v (m/s)') -40 -30 -20 -10 0 10 20 -10 -5 0 5 10 15 20 25 30 35 40 x (m) y (m) 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 t (s) v (m/s)
Chapter 5: Solved Problems 17 Problem 17 Script File: T=[5840 22400 13260 9400 3100 4300 28000]; L=[1 13400 150 108 0.0004 0.15 34000]; RR=[1 7.8 3.5 3.7 0.18 0.76 8]; LL=RR.^2.*(T/5840).^4; han=loglog(T,L,'*',T,LL,'o'); set(gca,'XDir','reverse') xlabel('Temperature (K)') ylabel('Relative Luminosity') 10 3 10 4 10 5 10 -4 10 -2 10 0 10 2 10 4 10 6 Temperature (K) Relative Luminosity
18 Chapter 5: Solved Problems Problem 18 Script File: t=0:0.1:8; x=0.41*t.^4-10.8*t.^3+64*t.^2-8.2*t+4.4; v=0.41*4*t.^3-10.8*3*t.^2+64*2*t-8.2; a=0.41*4*3*t.^2-10.8*3*2*t+64*2; subplot(3,1,1) plot(t,x) xlabel('Time (s)') ylabel('Position (m)') subplot(3,1,2) plot(t,v) xlabel('Time (s)') ylabel('Velocity (m/s)') subplot(3,1,3) plot(t,a) xlabel('Time (s)') ylabel('Acceleration (m/s^2)')
Chapter 5: Solved Problems 19 0 1 2 3 4 5 6 7 8 0 100 200 300 400 500 Time (s) Position (m) 0 1 2 3 4 5 6 7 8 -300 -200 -100 0 100 200 Time (s) Velocity (m/s) 0 1 2 3 4 5 6 7 8 -100 -50 0 50 100 150 Time (s) Acceleration (m/s 2 )
20 Chapter 5: Solved Problems Problem 19 Script File: F=[0 13345 26689 40479 42703 43592 44482 44927 45372 46276 47908 49035 50265 53213 56161]; L=[25 25.037 25.073 25.113 25.122 25.125 25.132 25.144 25.164 25.208 25.409 25.646 26.084 27.398 29.150]; r=0.0064; L0=25; A0=pi*r^2; sigmaE=F./A0; epsE=(L-L0)./L0; sigmaT=sigmaE.*L./L0; epsT=log(L./L0); plot(epsE,sigmaE,'-k',epsT,sigmaT,'--k') xlabel('Normal Strain','fontsize',16) ylabel('Normal Stress (MPa)','fontsize',16) text(0.1,390e6,'Engineering stress-strain curve','fon- tsize',14) text(0.06,520e6,'Engineering stress-strain curve','fon- tsize',14) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0 1 2 3 4 5 6 x 10 8 Normal Strain Normal Stress (MPa) Engineering stress-strain curve Engineering stress-strain curve
Chapter 5: Solved Problems 21 Problem 20 Script File: Q1=4; Q2=5; PG=2:1:60; AV1=Q1./sqrt(PG); AV2=Q2./sqrt(PG); plot(PG,AV1,'-',PG,AV2,'--') xlabel('PG (mmHG)') ylabel('Area (cm^2)') legend('Q=4 L/min','Q=5 L/min') 0 10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 3.5 4 PG (mmHG) Area (cm 2 ) Q=4 L/min Q=5 L/min
22 Chapter 5: Solved Problems Problem 21 R=80; C=18E-6; L=260E-3;Vm=10; k=1:0.01:4; f=10.^k; w=2*pi*f; Is=Vm./sqrt(R^2+(w*L-1./(w*C)).^2); semilogx(f,Is) xlabel('fd (Hz)') ylabel('I (A)') 10 1 10 2 10 3 10 4 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 fd (Hz) I (A)
Chapter 5: Solved Problems 23 Problem 22 m=5.3E-26; kB=1.38E-23; T1=300; T2=80; v=0:20:1000; K=m/(2*pi*kB); Kex=m/(2*kB); vsq=v.^2; Nv1=4*pi*(K/T1)^(3/2)*vsq.*exp(-Kex/T1*vsq); Nv2=4*pi*(K/T2)^(3/2)*vsq.*exp(-Kex/T2*vsq); plot(v,Nv1,v,Nv2) xlabel('v (m/s)') ylabel('N(v)') legend('T=300 K','T=80 K') 0 100 200 300 400 500 600 700 800 900 1000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 -3 v (m/s) N(v) T=300 K T=80 K
24 Chapter 5: Solved Problems Problem 23 Script File: R=4; L=1.3; V=12; t1=0:0.01:0.5; t2=0.5:0.01:2; i1=V*(1-exp(-R*t1./L))/R; i2=exp(-R*t2./L)*V.*(exp(0.5*R/L)-1)/R; plot(t1,i1,t2,i2) xlabel('Time (s)') ylabel('Current (A)') 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 2.5 Time (s) Current (A)
Chapter 5: Solved Problems 25 Problem 24 t=0.2; c=1.5; x=linspace(0,c,100); xf=x/c; yt=t*c/0.2*(0.2968*sqrt(xf)-0.126*xf- 0.3516*xf.^2+0.2843*xf.^3-0.1015*xf.^4); yb=-t*c/0.2*(0.2968*sqrt(xf)-0.126*xf- 0.3516*xf.^2+0.2843*xf.^3-0.1015*xf.^4); plot(x,yt,x,yb) axis([0 1.5 -0.2 0.2]) xlabel('x (m)') ylabel('y (m)') 0 0.5 1 1.5 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 x (m) y (m)
26 Chapter 5: Solved Problems Problem 25 Script File: Ginf=5000; c=0.05; tau1=0.05; tau2=500; L=-4:0.1:3; w=10.^L; Gp=Ginf*(1+c*log((1+(w*tau2).^2)./(1+(w*tau1).^2))/2); Gpp=c*Ginf*(atan(w*tau2)-atan(w*tau1)); subplot(2,1,1) semilogx(w,Gp) xlabel('Frequncy (1/s)') ylabel('Storage Modulus (psi)') subplot(2,1,2) semilogx(w,Gpp) xlabel('Frequncy (1/s)') ylabel('Loss Modulus (psi)') 10 -4 10 -2 10 0 10 2 10 4 5000 5500 6000 6500 7000 7500 Frequncy (1/s) Storage Modulus (psi) 10 -4 10 -2 10 0 10 2 10 4 0 50 100 150 200 250 300 350 400 Frequncy (1/s) Loss Modulus (psi)
Chapter 5: Solved Problems 27 Problem 26 Script File: F0=12; wn=10; w=12; t=linspace(0,10,1000); x=2*F0*sin((wn-w)*t/2).*sin((wn+w)*t/2)./(wn^2-w^2); plot(t,x) xlabel('Time (s)') ylabel('Position (m)') 0 1 2 3 4 5 6 7 8 9 10 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Time (s) Position (m)
28 Chapter 5: Solved Problems Problem 27 I0=1E-14; K=30E-3; vS=1.5;R=1200; vD1=linspace(0,0.76,100); vD2=linspace(0,1.5,100); iD1=I0*(exp(vD1/K)-1); iD2=-vD2/R+vS/R; plot(vD1,iD1,vD2,iD2) xlabel('vD (V)') ylabel('iD (A)') Estimate: V, A 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10 -3 vD (V) iD (A) vD 0.75 = iD 0.61 =
Chapter 5: Solved Problems 29 Problem 28 Script File: R=0.08208; a=1.39; b=0.0391; n=1; T=300; V=0.08:0.02:6; p=n*R*T./(V-n*b)-n^2*a./V.^2; PVRT=p.*V/(R*T); plot(p,PVRT); xlabel('Pressure (atm)') ylabel('PV over RT') The response does not agree with the ideal gas equation. 0 50 100 150 200 250 300 350 400 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Pressure (atm) PV over RT
30 Chapter 5: Solved Problems Problem 29 th=-20:0.1:20; aL1=pi*10*sind(th); Ith1=(sin(aL1)./aL1).^2; aL2=pi*5*sind(th); Ith2=(sin(aL2)./aL2).^2; aL3=pi*sind(th); Ith3=(sin(aL3)./aL3).^2; plot(th,Ith1,th,Ith2,th,Ith3) xlabel('Theta (deg)') ylabel('I/Imax') legend('10 lambda','5 lambda','lambda') -20 -15 -10 -5 0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Theta (deg) I/Imax 10 λ 5 λ λ
Chapter 5: Solved Problems 31 Problem 30 Script file: d1=0.875; d2=0.75; L1=50*12; L2=40*12; th=30:1:85; R=(L1-L2*cotd(th))/d1^4+L2./(d2^4*sind(th)); plot(th,R) [Rmin el]=min(R); Rmin ThetaofRmin=th(el) s=L2/tand(th(el))/12 xlabel('Angle (deg)') ylabel('R/K') Command Window: Rmin = 2.3007e+003 ThetaofRmin = 57 s = 25.9763 30 40 50 60 70 80 90 2300 2350 2400 2450 2500 2550 2600 2650 Angle (deg) R/K
32 Chapter 5: Solved Problems Problem 31 Script File: EI=200E9*384E-6; L=20; w=5400; M=200000; x1=0:0.1:10; x2=10.1:0.1:20; K1=w/(384*EI); K2=M/(6*EI*L); y1=-K1*x1.*(16*x1.^3-24*L*x1.^2+9*L^3)+K2*x1.*(x1.^2- 3*L*x1+2*L^2); y2=-K1*L*(8*x2.^3-24*L*x2.^2+17*L^2*x2-L^3)+K2*x2.*(x2.^2- 3*L*x2+2*L^2); plot(x1,y1,x2,y2) xlabel('x (m)') ylabel('y (m)') 0 2 4 6 8 10 12 14 16 18 20 -10 -8 -6 -4 -2 0 2 4 x 10 -3 x (m) y (m)
Chapter 5: Solved Problems 33 Problem 32 R=8.3145; T=[100:100:400]; V=linspace(1,10,100); p1=R*T(1)./V; p2=R*T(2)./V; p3=R*T(3)./V; p4=R*T(4)./V; plot(V,p1,V,p2,V,p3,V,p4) xlabel('V (m^3)') ylabel('P (Pa)') legend('T=100K','T=200K','T=300K','T=400K') 1 2 3 4 5 6 7 8 9 10 0 500 1000 1500 2000 2500 3000 3500 V (m3 ) P (Pa) T=100K T=200K T=300K T=400K
34 Chapter 5: Solved Problems Problem 33 V=12; R2=120; R3=250; R4=250; R1=linspace(0,500,100); VABa=V*(R2./(R1+R2)-R4/(R3+R4)); subplot(2,1,1) plot(R1,VABa) xlabel('R1 (Ohm)') ylabel('vAB (V)') R1b=120; R2b=linspace(0,500,100); VABb=V*(R2b./(R1b+R2b)-R4/(R3+R4)); subplot(2,1,2) plot(R2b,VABb) xlabel('R2 (Ohm)') ylabel('vAB (V)') 0 50 100 150 200 250 300 350 400 450 500 -4 -2 0 2 4 6 R1 (Ohm) vAB (V) 0 50 100 150 200 250 300 350 400 450 500 -6 -4 -2 0 2 4 R2 (Ohm) vAB (V)
Chapter 5: Solved Problems 35 Problem 34 L=0.2; C=2E-6; LC=L*C; % Part a R1a=1500; R2a=500:20:2000; fa=1/(2*pi)*sqrt(LC*(R1a^2*C-L)./(R2a.^2*C-L)); subplot(2,1,1) plot(R2a,fa) xlabel('R2 (ohm)') ylabel('f (1/s)') % Part b R2b=1500; R1b=500:20:2000; fb=1/(2*pi)*sqrt(LC*(R1b.^2*C-L)./(R2b^2*C-L)); subplot(2,1,2) plot(R1b,fb) xlabel('R1 (ohm)') ylabel('f (1/s)')
36 Chapter 5: Solved Problems 500 1000 1500 2000 0.5 1 1.5 2 2.5 3 3.5 4 x 10 -4 R2 (ohm) f (1/s) 500 1000 1500 2000 2 4 6 8 10 12 14 x 10 -5 R1 (ohm) f (1/s)
Chapter 5: Solved Problems 37 Problem 35 x=linspace(-2*pi,2*pi); x2=linspace(-pi,1*pi,100); x5=linspace(-2*pi,2*pi,100); x7=linspace(-2*pi,2*pi,100); f5=factorial(5); f7=factorial(7); f9=factorial(9); f11=factorial(11); f13=factorial(13); y=sin(x); y1=x; y2=x2-x2.^3/6; y5=x5-x5.^3/6+x5.^5/f5-x5.^7/f7+x5.^9/f9; y7=x7-x7.^3/6+x7.^5/f5-x7.^7/f7+x7.^9/f9-x7.^11/f11+x7.^13/ f13; plot(x,y,x,y1,'-.',x2,y2,'.',x5,y5,'--') %plot(x,y,x2,y2,x4,y4,x6,y6) axis([-8 8 -2 2]) -8 -6 -4 -2 0 2 4 6 8 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x sin(x) sin(x) One term Two terms Three terms
38 Chapter 5: Solved Problems

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Gilat_ch05.pdf

  • 1. 1 Chapter 5 Solved Problems Problem 1 Script File: x=linspace(-3,5,200); y=(x+5).^2./(4+3*x.^2); plot(x,y) xlabel('x') ylabel('y') -3 -2 -1 0 1 2 3 4 5 0 1 2 3 4 5 6 7 x y
  • 2. 2 Chapter 5: Solved Problems Problem 2 Script File: fplot('5*sin(x)/(x+exp(-0.75*x))',[-5 10]) xlabel('x') ylabel('y') -5 0 5 10 -4 -3 -2 -1 0 1 2 3 x y
  • 3. Chapter 5: Solved Problems 3 Problem 3 Script file: x1=linspace(0,3,200); y1=(x1+1).*(x1-2).*(2*x1-0.25)-exp(x1); x2=linspace(-3,6,200); y2=(x2+1).*(x2-2).*(2*x2-0.25)-exp(x2); plot(x1,y1) xlabel('x') ylabel('y') figure plot(x2,y2) xlabel('x') ylabel('y') 0 0.5 1 1.5 2 2.5 3 -10 -8 -6 -4 -2 0 2 4 x y -3 -2 -1 0 1 2 3 4 5 6 -80 -60 -40 -20 0 20 40 x y
  • 4. 4 Chapter 5: Solved Problems Problem 4 Script File: plot('sqrt(abs(cos(3*x)))+sin(4*x)^2',[-2 2]) xlabel('x') ylabel('y')) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x y
  • 5. Chapter 5: Solved Problems 5 Problem 5 Script File: fplot('exp(2*sin(0.4*x))*5*cos(4*x)',[-20 30]) xlabel('x') ylabel('y') -20 -15 -10 -5 0 5 10 15 20 25 30 -40 -30 -20 -10 0 10 20 30 40 x y
  • 6. 6 Chapter 5: Solved Problems Problem 6 Script File: t=linspace(0,2*pi,100); x=1.5*sin(5*t); y=1.5*cos(3*t); plot(x,y) axis([-2 2 -2 2]) xlabel('x') ylabel('y') -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x y
  • 7. Chapter 5: Solved Problems 7 Problem 7 x1=-4:0.05:-1.1; x2=-0.9:0.05:3; y1=(x1.^2+3*x1+3)./(0.8*(x1+1)); y2=(x2.^2+3*x2+3)./(0.8*(x2+1)); plot(x1,y1,x2,y2) xlabel('x') ylabel('y') -4 -3 -2 -1 0 1 2 3 -15 -10 -5 0 5 10 15 x y
  • 8. 8 Chapter 5: Solved Problems Problem 8 t1=linspace(-30,-1.6,500); t2=linspace(-0.6,40,500); x1=3*t1./(1+t1.^3); y1=3*t1.^2./(1+t1.^3); x2=3*t2./(1+t2.^3); y2=3*t2.^2./(1+t2.^3); plot(x1,y1,x2,y2) xlabel('x') ylabel('y') -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x y
  • 9. Chapter 5: Solved Problems 9 Problem 9 x1=-6:0.05:-2.1; x2=-1.9:0.05:2.8; x3=3.2:0.05:6; y1=(x1.^2-4*x1-7)./(x1.^2-x1-6); y2=(x2.^2-4*x2-7)./(x2.^2-x2-6); y3=(x3.^2-4*x3-7)./(x3.^2-x3-6); plot(x1,y1,x2,y2,x3,y3) %axis([-10 10 -30 30]) xlabel('x') ylabel('y') -6 -4 -2 0 2 4 6 -10 -5 0 5 10 15 x y
  • 10. 10 Chapter 5: Solved Problems Problem 10 r=1.5; t=linspace(0,4*pi,300); x=r*(t-sin(t)); y=r*(1-cos(t)); plot(x,y) xlabel('x') ylabel('y') 0 2 4 6 8 10 12 14 16 18 20 0 0.5 1 1.5 2 2.5 3 x y
  • 11. Chapter 5: Solved Problems 11 Problem 11 x=linspace(-pi,pi,200); f=cos(x).*sin(2*x); df=2*cos(2*x).*cos(x)-sin(2*x).*sin(x); plot(x,f,x,df,'--') xlabel('x') ylabel('f(x), df(x)/dx') legend('f(x)','df(x)/dx') -4 -3 -2 -1 0 1 2 3 4 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x f(x), df(x)/dx f(x) df(x)/dx
  • 12. 12 Chapter 5: Solved Problems Problem 12 Command Window: >> fplot('693.8-68.8*cosh(x/99.7)',[-300 300]) -300 -200 -100 0 100 200 300 -100 0 100 200 300 400 500 600 700
  • 13. Chapter 5: Solved Problems 13 Problem 13 Script File: vs=12; rs=2.5; RL=1:0.05:10; P=vs^2*RL./(RL+rs).^2; plot(RL,P) xlabel('R_L (Omega)') ylabel('P (W)') 1 2 3 4 5 6 7 8 9 10 9 10 11 12 13 14 15 RL (Ω) P (W)
  • 14. 14 Chapter 5: Solved Problems Problem 14 Script File: t=0:0.01:4; tDay=8+t; vA=27; vB=14; xA=-36+vA*cosd(30)*t; yA=12-vA*sind(30)*t; xB=-18+vB*cosd(70)*t; yB=-45+vB*sind(70)*t; dis=sqrt((xB-xA).^2+(yB-yA).^2); plot(tDay,dis) xlabel('Time of the Day') ylabel('Distance Between the Ships (mi)') 8 8.5 9 9.5 10 10.5 11 11.5 12 10 20 30 40 50 60 70 80 Time of the Day Distance Between the Ships (mi)
  • 15. Chapter 5: Solved Problems 15 Problem 15 Kab=1.6; Kel=0.45; C=140; t=0:0.05:10; Cp=C*Kab/(Kab-Kel)*(exp(-Kel*t)-exp(-Kab*t)); plot(t,Cp) xlabel('t (h)') ylabel('Cp (mg/L)') 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 70 80 90 t (h) Cp (mg/L)
  • 16. 16 Chapter 5: Solved Problems Problem 16 Script File: t=0:0.1:20; r= 20+ 30*(1-exp(-0.1*t)); th=pi*(1-exp(-0.2*t)); x=r.*cos(th); y=r.*sin(th); thdot=pi*0.2*exp(-0.2*t); v=r.*thdot; plot(x,y) axis equal xlabel('x (m)') ylabel('y (m)') figure plot(t,v) xlabel('t (s)') ylabel('v (m/s)') -40 -30 -20 -10 0 10 20 -10 -5 0 5 10 15 20 25 30 35 40 x (m) y (m) 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 t (s) v (m/s)
  • 17. Chapter 5: Solved Problems 17 Problem 17 Script File: T=[5840 22400 13260 9400 3100 4300 28000]; L=[1 13400 150 108 0.0004 0.15 34000]; RR=[1 7.8 3.5 3.7 0.18 0.76 8]; LL=RR.^2.*(T/5840).^4; han=loglog(T,L,'*',T,LL,'o'); set(gca,'XDir','reverse') xlabel('Temperature (K)') ylabel('Relative Luminosity') 10 3 10 4 10 5 10 -4 10 -2 10 0 10 2 10 4 10 6 Temperature (K) Relative Luminosity
  • 18. 18 Chapter 5: Solved Problems Problem 18 Script File: t=0:0.1:8; x=0.41*t.^4-10.8*t.^3+64*t.^2-8.2*t+4.4; v=0.41*4*t.^3-10.8*3*t.^2+64*2*t-8.2; a=0.41*4*3*t.^2-10.8*3*2*t+64*2; subplot(3,1,1) plot(t,x) xlabel('Time (s)') ylabel('Position (m)') subplot(3,1,2) plot(t,v) xlabel('Time (s)') ylabel('Velocity (m/s)') subplot(3,1,3) plot(t,a) xlabel('Time (s)') ylabel('Acceleration (m/s^2)')
  • 19. Chapter 5: Solved Problems 19 0 1 2 3 4 5 6 7 8 0 100 200 300 400 500 Time (s) Position (m) 0 1 2 3 4 5 6 7 8 -300 -200 -100 0 100 200 Time (s) Velocity (m/s) 0 1 2 3 4 5 6 7 8 -100 -50 0 50 100 150 Time (s) Acceleration (m/s 2 )
  • 20. 20 Chapter 5: Solved Problems Problem 19 Script File: F=[0 13345 26689 40479 42703 43592 44482 44927 45372 46276 47908 49035 50265 53213 56161]; L=[25 25.037 25.073 25.113 25.122 25.125 25.132 25.144 25.164 25.208 25.409 25.646 26.084 27.398 29.150]; r=0.0064; L0=25; A0=pi*r^2; sigmaE=F./A0; epsE=(L-L0)./L0; sigmaT=sigmaE.*L./L0; epsT=log(L./L0); plot(epsE,sigmaE,'-k',epsT,sigmaT,'--k') xlabel('Normal Strain','fontsize',16) ylabel('Normal Stress (MPa)','fontsize',16) text(0.1,390e6,'Engineering stress-strain curve','fon- tsize',14) text(0.06,520e6,'Engineering stress-strain curve','fon- tsize',14) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0 1 2 3 4 5 6 x 10 8 Normal Strain Normal Stress (MPa) Engineering stress-strain curve Engineering stress-strain curve
  • 21. Chapter 5: Solved Problems 21 Problem 20 Script File: Q1=4; Q2=5; PG=2:1:60; AV1=Q1./sqrt(PG); AV2=Q2./sqrt(PG); plot(PG,AV1,'-',PG,AV2,'--') xlabel('PG (mmHG)') ylabel('Area (cm^2)') legend('Q=4 L/min','Q=5 L/min') 0 10 20 30 40 50 60 0.5 1 1.5 2 2.5 3 3.5 4 PG (mmHG) Area (cm 2 ) Q=4 L/min Q=5 L/min
  • 22. 22 Chapter 5: Solved Problems Problem 21 R=80; C=18E-6; L=260E-3;Vm=10; k=1:0.01:4; f=10.^k; w=2*pi*f; Is=Vm./sqrt(R^2+(w*L-1./(w*C)).^2); semilogx(f,Is) xlabel('fd (Hz)') ylabel('I (A)') 10 1 10 2 10 3 10 4 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 fd (Hz) I (A)
  • 23. Chapter 5: Solved Problems 23 Problem 22 m=5.3E-26; kB=1.38E-23; T1=300; T2=80; v=0:20:1000; K=m/(2*pi*kB); Kex=m/(2*kB); vsq=v.^2; Nv1=4*pi*(K/T1)^(3/2)*vsq.*exp(-Kex/T1*vsq); Nv2=4*pi*(K/T2)^(3/2)*vsq.*exp(-Kex/T2*vsq); plot(v,Nv1,v,Nv2) xlabel('v (m/s)') ylabel('N(v)') legend('T=300 K','T=80 K') 0 100 200 300 400 500 600 700 800 900 1000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 -3 v (m/s) N(v) T=300 K T=80 K
  • 24. 24 Chapter 5: Solved Problems Problem 23 Script File: R=4; L=1.3; V=12; t1=0:0.01:0.5; t2=0.5:0.01:2; i1=V*(1-exp(-R*t1./L))/R; i2=exp(-R*t2./L)*V.*(exp(0.5*R/L)-1)/R; plot(t1,i1,t2,i2) xlabel('Time (s)') ylabel('Current (A)') 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 2.5 Time (s) Current (A)
  • 25. Chapter 5: Solved Problems 25 Problem 24 t=0.2; c=1.5; x=linspace(0,c,100); xf=x/c; yt=t*c/0.2*(0.2968*sqrt(xf)-0.126*xf- 0.3516*xf.^2+0.2843*xf.^3-0.1015*xf.^4); yb=-t*c/0.2*(0.2968*sqrt(xf)-0.126*xf- 0.3516*xf.^2+0.2843*xf.^3-0.1015*xf.^4); plot(x,yt,x,yb) axis([0 1.5 -0.2 0.2]) xlabel('x (m)') ylabel('y (m)') 0 0.5 1 1.5 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 x (m) y (m)
  • 26. 26 Chapter 5: Solved Problems Problem 25 Script File: Ginf=5000; c=0.05; tau1=0.05; tau2=500; L=-4:0.1:3; w=10.^L; Gp=Ginf*(1+c*log((1+(w*tau2).^2)./(1+(w*tau1).^2))/2); Gpp=c*Ginf*(atan(w*tau2)-atan(w*tau1)); subplot(2,1,1) semilogx(w,Gp) xlabel('Frequncy (1/s)') ylabel('Storage Modulus (psi)') subplot(2,1,2) semilogx(w,Gpp) xlabel('Frequncy (1/s)') ylabel('Loss Modulus (psi)') 10 -4 10 -2 10 0 10 2 10 4 5000 5500 6000 6500 7000 7500 Frequncy (1/s) Storage Modulus (psi) 10 -4 10 -2 10 0 10 2 10 4 0 50 100 150 200 250 300 350 400 Frequncy (1/s) Loss Modulus (psi)
  • 27. Chapter 5: Solved Problems 27 Problem 26 Script File: F0=12; wn=10; w=12; t=linspace(0,10,1000); x=2*F0*sin((wn-w)*t/2).*sin((wn+w)*t/2)./(wn^2-w^2); plot(t,x) xlabel('Time (s)') ylabel('Position (m)') 0 1 2 3 4 5 6 7 8 9 10 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Time (s) Position (m)
  • 28. 28 Chapter 5: Solved Problems Problem 27 I0=1E-14; K=30E-3; vS=1.5;R=1200; vD1=linspace(0,0.76,100); vD2=linspace(0,1.5,100); iD1=I0*(exp(vD1/K)-1); iD2=-vD2/R+vS/R; plot(vD1,iD1,vD2,iD2) xlabel('vD (V)') ylabel('iD (A)') Estimate: V, A 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10 -3 vD (V) iD (A) vD 0.75 = iD 0.61 =
  • 29. Chapter 5: Solved Problems 29 Problem 28 Script File: R=0.08208; a=1.39; b=0.0391; n=1; T=300; V=0.08:0.02:6; p=n*R*T./(V-n*b)-n^2*a./V.^2; PVRT=p.*V/(R*T); plot(p,PVRT); xlabel('Pressure (atm)') ylabel('PV over RT') The response does not agree with the ideal gas equation. 0 50 100 150 200 250 300 350 400 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Pressure (atm) PV over RT
  • 30. 30 Chapter 5: Solved Problems Problem 29 th=-20:0.1:20; aL1=pi*10*sind(th); Ith1=(sin(aL1)./aL1).^2; aL2=pi*5*sind(th); Ith2=(sin(aL2)./aL2).^2; aL3=pi*sind(th); Ith3=(sin(aL3)./aL3).^2; plot(th,Ith1,th,Ith2,th,Ith3) xlabel('Theta (deg)') ylabel('I/Imax') legend('10 lambda','5 lambda','lambda') -20 -15 -10 -5 0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Theta (deg) I/Imax 10 λ 5 λ λ
  • 31. Chapter 5: Solved Problems 31 Problem 30 Script file: d1=0.875; d2=0.75; L1=50*12; L2=40*12; th=30:1:85; R=(L1-L2*cotd(th))/d1^4+L2./(d2^4*sind(th)); plot(th,R) [Rmin el]=min(R); Rmin ThetaofRmin=th(el) s=L2/tand(th(el))/12 xlabel('Angle (deg)') ylabel('R/K') Command Window: Rmin = 2.3007e+003 ThetaofRmin = 57 s = 25.9763 30 40 50 60 70 80 90 2300 2350 2400 2450 2500 2550 2600 2650 Angle (deg) R/K
  • 32. 32 Chapter 5: Solved Problems Problem 31 Script File: EI=200E9*384E-6; L=20; w=5400; M=200000; x1=0:0.1:10; x2=10.1:0.1:20; K1=w/(384*EI); K2=M/(6*EI*L); y1=-K1*x1.*(16*x1.^3-24*L*x1.^2+9*L^3)+K2*x1.*(x1.^2- 3*L*x1+2*L^2); y2=-K1*L*(8*x2.^3-24*L*x2.^2+17*L^2*x2-L^3)+K2*x2.*(x2.^2- 3*L*x2+2*L^2); plot(x1,y1,x2,y2) xlabel('x (m)') ylabel('y (m)') 0 2 4 6 8 10 12 14 16 18 20 -10 -8 -6 -4 -2 0 2 4 x 10 -3 x (m) y (m)
  • 33. Chapter 5: Solved Problems 33 Problem 32 R=8.3145; T=[100:100:400]; V=linspace(1,10,100); p1=R*T(1)./V; p2=R*T(2)./V; p3=R*T(3)./V; p4=R*T(4)./V; plot(V,p1,V,p2,V,p3,V,p4) xlabel('V (m^3)') ylabel('P (Pa)') legend('T=100K','T=200K','T=300K','T=400K') 1 2 3 4 5 6 7 8 9 10 0 500 1000 1500 2000 2500 3000 3500 V (m3 ) P (Pa) T=100K T=200K T=300K T=400K
  • 34. 34 Chapter 5: Solved Problems Problem 33 V=12; R2=120; R3=250; R4=250; R1=linspace(0,500,100); VABa=V*(R2./(R1+R2)-R4/(R3+R4)); subplot(2,1,1) plot(R1,VABa) xlabel('R1 (Ohm)') ylabel('vAB (V)') R1b=120; R2b=linspace(0,500,100); VABb=V*(R2b./(R1b+R2b)-R4/(R3+R4)); subplot(2,1,2) plot(R2b,VABb) xlabel('R2 (Ohm)') ylabel('vAB (V)') 0 50 100 150 200 250 300 350 400 450 500 -4 -2 0 2 4 6 R1 (Ohm) vAB (V) 0 50 100 150 200 250 300 350 400 450 500 -6 -4 -2 0 2 4 R2 (Ohm) vAB (V)
  • 35. Chapter 5: Solved Problems 35 Problem 34 L=0.2; C=2E-6; LC=L*C; % Part a R1a=1500; R2a=500:20:2000; fa=1/(2*pi)*sqrt(LC*(R1a^2*C-L)./(R2a.^2*C-L)); subplot(2,1,1) plot(R2a,fa) xlabel('R2 (ohm)') ylabel('f (1/s)') % Part b R2b=1500; R1b=500:20:2000; fb=1/(2*pi)*sqrt(LC*(R1b.^2*C-L)./(R2b^2*C-L)); subplot(2,1,2) plot(R1b,fb) xlabel('R1 (ohm)') ylabel('f (1/s)')
  • 36. 36 Chapter 5: Solved Problems 500 1000 1500 2000 0.5 1 1.5 2 2.5 3 3.5 4 x 10 -4 R2 (ohm) f (1/s) 500 1000 1500 2000 2 4 6 8 10 12 14 x 10 -5 R1 (ohm) f (1/s)
  • 37. Chapter 5: Solved Problems 37 Problem 35 x=linspace(-2*pi,2*pi); x2=linspace(-pi,1*pi,100); x5=linspace(-2*pi,2*pi,100); x7=linspace(-2*pi,2*pi,100); f5=factorial(5); f7=factorial(7); f9=factorial(9); f11=factorial(11); f13=factorial(13); y=sin(x); y1=x; y2=x2-x2.^3/6; y5=x5-x5.^3/6+x5.^5/f5-x5.^7/f7+x5.^9/f9; y7=x7-x7.^3/6+x7.^5/f5-x7.^7/f7+x7.^9/f9-x7.^11/f11+x7.^13/ f13; plot(x,y,x,y1,'-.',x2,y2,'.',x5,y5,'--') %plot(x,y,x2,y2,x4,y4,x6,y6) axis([-8 8 -2 2]) -8 -6 -4 -2 0 2 4 6 8 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x sin(x) sin(x) One term Two terms Three terms
  • 38. 38 Chapter 5: Solved Problems