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7/11/14 Homework #2 Renan Santos

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Names of people you worked with:

Websites you used:

By writing or typing your name below you affirm that all of the work

contained herein is your own, and was not copied or copied and altered.

RENAN SANTOS

Lab time (eg tues 10am): Note: Change the homework number and name at the top of the page by selecting view->header and foot. Failure to change the name and to sign this page will result in a 5% point penalty.


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Problem 1

Comments for grader/additional information (if any)

Script File (should include pseudo code as comments) clear all clc

% Creating Variables ts1=linspace(0,1,100); ts2=linspace(0,1,100);

%calculating array length length(ts1) length(ts2)

%Checking the first and last elements of ts1 and ts2 ts1(1) ts2(1) ts1(end) ts2(end)

%calcuating the sum, the minimum value and the average number of ts1 sum(ts1) min(ts1) mean(ts1)

%Creating tsRev tsRev=linspace(1,0,100);

%Checking the first and last elements of tsRev tsRev(1) tsRev(end)

Function File (if applicable)

Command Window Output (cut and paste output here) ans = 100 ans = 100


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ans = 0 ans = 0 ans = 1 ans = 1 ans = 50.0000 ans = 0 ans = 0.5000 ans = 1 ans = 0


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Plot Window Output (you can save the plot and include it here – save it

as a png, not a fig, or use a screen grab mac windows)

http://graphicssoft.about.com/od/screencapturemac/ht/macscreenshot.htm

http://graphicssoft.about.com/cs/general/ht/winscreenshot.htm


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Problem 2


Script File (should include pseudo code as comments) clear all clc

% Creating Variables ts1=linspace(0,1,100); ts2=linspace(0,1,100);

%calculating array length length(ts1) length(ts2)

%Checking the first and last elements of ts1 and ts2 ts1(1) ts2(1) ts1(end) ts2(end)

%calcuating the sum, the minimum value and the average number of ts1 sum(ts1) min(ts1) mean(ts1)

%Creating tsRev tsRev=linspace(1,0,100);

%Checking the first and last elements of tsRev tsRev(1)

%Prob 2 ts3=ts1(3) ts1to3=ts1(1:3) ts3to1=ts1(3:-1:1) %We already have a tsRev variable tsSkip=ts1(1:2:end) length(tsSkip) ts1=ts1+1 ts1=ts1+1 ts1=ts1+1 ts1(1) ts1(end)


Command Window Output (cut and paste output here)


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ans = 100 ans = 100 ans = 0 ans = 0 ans = 1 ans = 1 ans = 50.0000 ans = 0 ans = 0.5000 ans =


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1 ts3 = 0.0202 ts1to3 = 0 0.0101 0.0202 ts3to1 = 0.0202 0.0101 0 tsSkip = Columns 1 through 11 0 0.0202 0.0404 0.0606 0.0808 0.1010 0.1212 0.1414 0.1616 0.1818 0.2020 Columns 12 through 22 0.2222 0.2424 0.2626 0.2828 0.3030 0.3232 0.3434 0.3636 0.3838 0.4040 0.4242 Columns 23 through 33 0.4444 0.4646 0.4848 0.5051 0.5253 0.5455 0.5657 0.5859 0.6061 0.6263 0.6465 Columns 34 through 44 0.6667 0.6869 0.7071 0.7273 0.7475 0.7677 0.7879 0.8081 0.8283 0.8485 0.8687 Columns 45 through 50 0.8889 0.9091 0.9293 0.9495 0.9697 0.9899


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ans = 50 ts1 = Columns 1 through 11 1.0000 1.0101 1.0202 1.0303 1.0404 1.0505 1.0606 1.0707 1.0808 1.0909 1.1010 Columns 12 through 22 1.1111 1.1212 1.1313 1.1414 1.1515 1.1616 1.1717 1.1818 1.1919 1.2020 1.2121 Columns 23 through 33 1.2222 1.2323 1.2424 1.2525 1.2626 1.2727 1.2828 1.2929 1.3030 1.3131 1.3232 Columns 34 through 44 1.3333 1.3434 1.3535 1.3636 1.3737 1.3838 1.3939 1.4040 1.4141 1.4242 1.4343 Columns 45 through 55 1.4444 1.4545 1.4646 1.4747 1.4848 1.4949 1.5051 1.5152 1.5253 1.5354 1.5455 Columns 56 through 66 1.5556 1.5657 1.5758 1.5859 1.5960 1.6061 1.6162 1.6263 1.6364 1.6465 1.6566 Columns 67 through 77 1.6667 1.6768 1.6869 1.6970 1.7071 1.7172 1.7273 1.7374 1.7475 1.7576 1.7677 Columns 78 through 88 1.7778 1.7879 1.7980 1.8081 1.8182 1.8283 1.8384 1.8485 1.8586 1.8687 1.8788


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Columns 89 through 99 1.8889 1.8990 1.9091 1.9192 1.9293 1.9394 1.9495 1.9596 1.9697 1.9798 1.9899 Column 100 2.0000 ts1 = Columns 1 through 11 2.0000 2.0101 2.0202 2.0303 2.0404 2.0505 2.0606 2.0707 2.0808 2.0909 2.1010 Columns 12 through 22 2.1111 2.1212 2.1313 2.1414 2.1515 2.1616 2.1717 2.1818 2.1919 2.2020 2.2121 Columns 23 through 33 2.2222 2.2323 2.2424 2.2525 2.2626 2.2727 2.2828 2.2929 2.3030 2.3131 2.3232 Columns 34 through 44 2.3333 2.3434 2.3535 2.3636 2.3737 2.3838 2.3939 2.4040 2.4141 2.4242 2.4343 Columns 45 through 55 2.4444 2.4545 2.4646 2.4747 2.4848 2.4949 2.5051 2.5152 2.5253 2.5354 2.5455 Columns 56 through 66 2.5556 2.5657 2.5758 2.5859 2.5960 2.6061 2.6162 2.6263 2.6364 2.6465 2.6566 Columns 67 through 77


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2.6667 2.6768 2.6869 2.6970 2.7071 2.7172 2.7273 2.7374 2.7475 2.7576 2.7677 Columns 78 through 88 2.7778 2.7879 2.7980 2.8081 2.8182 2.8283 2.8384 2.8485 2.8586 2.8687 2.8788 Columns 89 through 99 2.8889 2.8990 2.9091 2.9192 2.9293 2.9394 2.9495 2.9596 2.9697 2.9798 2.9899 Column 100 3.0000 ts1 = Columns 1 through 11 3.0000 3.0101 3.0202 3.0303 3.0404 3.0505 3.0606 3.0707 3.0808 3.0909 3.1010 Columns 12 through 22 3.1111 3.1212 3.1313 3.1414 3.1515 3.1616 3.1717 3.1818 3.1919 3.2020 3.2121 Columns 23 through 33 3.2222 3.2323 3.2424 3.2525 3.2626 3.2727 3.2828 3.2929 3.3030 3.3131 3.3232 Columns 34 through 44 3.3333 3.3434 3.3535 3.3636 3.3737 3.3838 3.3939 3.4040 3.4141 3.4242 3.4343 Columns 45 through 55 3.4444 3.4545 3.4646 3.4747 3.4848 3.4949 3.5051 3.5152 3.5253 3.5354 3.5455 Columns 56 through 66


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3.5556 3.5657 3.5758 3.5859 3.5960 3.6061 3.6162 3.6263 3.6364 3.6465 3.6566 Columns 67 through 77 3.6667 3.6768 3.6869 3.6970 3.7071 3.7172 3.7273 3.7374 3.7475 3.7576 3.7677 Columns 78 through 88 3.7778 3.7879 3.7980 3.8081 3.8182 3.8283 3.8384 3.8485 3.8586 3.8687 3.8788 Columns 89 through 99 3.8889 3.8990 3.9091 3.9192 3.9293 3.9394 3.9495 3.9596 3.9697 3.9798 3.9899 Column 100 4.0000 ans = 3 ans = 4 >>






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Problem 3


Script File (should include pseudo code as comments) clc clear all

%Given x values x=linspace(1,10,30);

%Calculating y y=(2*x.^3)./(4*x+3);

%Calculating z z=2*(x+3)+(10*x+2)./(3*x.^2);

%Printing Results plot(x,y,'r') xlabel('x') ylabel('y') hold on plot(x,z,'k') xlabel('x') ylabel('y')


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Problem 4



%Declaring Variables A=input('Input the value for the variable A:'); B=input('Input the value for the variable B:'); aux=A;

%Printing values before the swap fprintf('Before the swap, the values of A are:\n'); disp(A) fprintf('Before the swap, the values of B are:\n'); disp(B)

%Swapping Values A=B; B=aux;

%Printing values after swapping fprintf('After the swap, the values of A are:\n'); disp(A) fprintf('After the swap, the values of B are:\n'); disp(B)


Command Window Output (cut and paste output here) Input the value for the variable A:5 Input the value for the variable B:6 Before the swap, the values of A are: 5 Before the swap, the values of B are: 6 After the swap, the values of A are: 6 After the swap, the values of B are: 5 >>


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Problem 5


Script File (should include pseudo code as comments) clc clear all clf

%Prob 5 PART A

%Declaring Domain t=(-5:0.05:1); %seconds

%Main Equation y=t.^2+3*t+4;

%Calculating the maximum and minimum values for y ymx=max(y); ymn=min(y);

%Printing values and plotting graph fprintf('The minimum and maximum values of y for the range of t

is %0.3f and %0.3f, respectively \n',ymn,ymx) plot(t,y,'k') xlabel('Time(sec)') ylabel('Distance(meters)') title('Tive vs Distance')

%Prob 5 PART B %Derivating the equation and we get: dy=2*t+3;


Command Window Output (cut and paste output here) The minimum and maximum values of y for the range of t is 1.750 and 14.000, respectively >>






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Problem 6



%Creating plots %Subplot 1 subplot(1,2,1); p=(1:1:100); %pressure (pascals) R=1.1; %Radius of the tank(meters) t=0.025; %thickness of the tank (meters) sigma=p.*R/(2*t); %stress (pascals) *Main Equation* plot(p,sigma,'b'); xlabel('Pressure(pascals)') ylabel('Stress(pascals)') title('Pressure vs Stress')

%Subplot 2 subplot(1,2,2); p=4; %Pascals R=2; %meters t=(0.01:0.03:3); %meters sigma=p*R*(2*t).^(-1); %stress (pascals) *Main Equation* plot(t,sigma,'k'); xlabel('Thickness(meters)') ylabel('Stress(pascals)') title('Thickness vs Stress')








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Problem 7



%Declaring Variables t=(0:0.2:3); % time (years) n1=1.2; %Scale Parameters n2=1.5; n3=2.5; b=1.2; %Shape parameter

%Main equation R1=exp(-(t./n1).^(b)); R2=exp(-(t./n2).^(b)); R3=exp(-(t./n3).^(b));

%Plotting graph plot(t,R1,'-r') hold on grid on plot(t,R2,'--k') hold on plot(t,R3,'-bo') legend('n1=1.2','n2=1.5','n3=2.5') xlabel('Time(years)') ylabel('Reliability') title('Time vs Reliability')








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Problem 8



%Declaring variables a=0.5; b=0.3; theta=linspace(0,10*pi,100); t=(0:1:1000);

%Main Equations

%Polar Coordinates r=a*exp(b*theta);

%Cartesian Coordinates x=a*exp(b*t).*cos(t); y=a*exp(b*t).*sin(t);

%PART A

%Creating subplots subplot(1,2,1); polar(theta,r) title('Polar Plot of a Spiral')

subplot(1,2,2); plot(x,y) title('Cartesian Plot of a Spiral')

%PART B p1=a*exp(b*0); %point p1 p2=a*exp(b*2*pi); %point p2 p3=a*exp(b*4*pi);%point p3 ratio1=p2/p1; ratio2=p3/p2;

%printing values fprintf('The ratio 1 is %0.3f and the ratio 2 is %0.3f

\n',ratio1,ratio2)


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Command Window Output (cut and paste output here) The ratio 1 is 6.586 and the ratio 2 is 6.586 >>






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Problem 9



%declaring variables m=150; %mass (kg) g=9.81; %gravity (m/s^2)

%PART A %declaring variables t=(0:1:35); %Time(seconds) c=13.5; %drag coefficient(kg/s) v=((g*m)./c)*(1-exp((-c*t)./m)); plot(t,v,'b'); hold on xlabel('Time(seconds)') ylabel('Velocity(m/s)') title('Time vs Velocity') vp=(g*m/c)*(1-exp(-c*12/m)); fprintf('The velocity at 12s with c= 13.5 is %0.2f m/s \n',vp)

%PART B c=9; %kg/s v1=((g*m)./c)*(1-exp((-c*t)./m)); plot(t,v1,'--k'); vp=(g*m/c)*(1-exp(-c*12/m)); fprintf('The velocity at 12s with c=9 is %0.2f m/s \n',vp) legend('c=13.5 kg/s','c=9 kg/s')


Command Window Output (cut and paste output here) The velocity at 12s with c= 13.5 is 71.98 m/s The velocity at 12s with c=9 is 83.92 m/s >>






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Problem 10



%declaring variables gin=5; %ksi c=0.05; t1=0.06; %seconds t2=500; %seconds w=(0.0001:1000); %s^-1

%Main Equations Gp=gin*(1+(c/2)*log((1+(w.*t2).^2)./(1+(w.*t1).^2))); Gdp=c*gin*(atan(w.*t2)-atan(w.*t1));

%Printing plots subplot(2,2,1) semilogx(w,Gp) title('Dynamic Storage Modulus (Gp)') xlabel('Frequency omega in inverse seconds') ylabel('Gp in ksi')

subplot(2,2,2) semilogx(w,Gdp) title('Dynamic Loss Modulus (Gdp)') xlabel('Frequency omega in inverse seconds') ylabel('Gdp in ksi')

subplot(2,2,3) plot(w,Gp) title('Dynamic Storage Modulus (Gp)') xlabel('Frequency omega in inverse seconds') ylabel('Gp in ksi')

subplot(2,2,4) plot(w,Gdp) title('Dynamic Loss Modulus (Gdp)') xlabel('Frequency omega in inverse seconds') ylabel('Gdp in ksi')


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