# teb11007 / 01_ME3255_repo

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Shell M MATLAB

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Problem 3
Problem 4
Problem 5
Problem 6
.bash_profile
.bashrc
A_66.m
Set_Defaults.m

# Answer to Homework Question

I hope to learn how to perform MATLAB functions more easily.

#Problem 3 (Mean_Std)

```A_66=zeros(6:6);
for i=1:6;
j=1:6;
A_66(i,j)=i*j;
end
fprintf('mean of A_66 = %1.2f\nstdev of A_66 = %1.2f\n',mean(A_66(:)),std(A_66(:)))```

Outputs:

mean of A_66 = 12.25

stdev of A_66 = 9.07

#Problem 4 (Energy Use)

```data=dlmread('US_energy_by_sector.csv',',',2,0);
h=figure();
plot(data(:,1),data(:,3),data(:,1),data(:,9));
%plotting residential energy consumption and transportational energy
%consumption from 1949 to 2016 in trillions of BTUs
set(0, 'defaultAxesFontSize', 16)
set(0,'defaultTextFontSize',14)
set(0,'defaultLineLineWidth',3)
set(gcf, 'Position', [200, 200, 1000, 800])
xlabel('Time (years)')
ylabel('Total Energy Consumed (trillions of BTUs)')
legend('Residential','Transportation','Location','northwest')
title('US Energy Consumption from 1949 to 2016')
saveas(h,'figure_01.png')```

![US Energy Use per Year from 1949-2016](./Problem 4/figure_01.png)

```rescum=cumsum(data(:,3))./1000000;%cumulative sum of residential energy
%consumption in quintillions of BTUs
transcum=cumsum(data(:,9))./1000000;%cumulative sum of transportational
%energy consumption in quintillions of BTUs
h=figure();
plot(data(:,1),rescum,data(:,1),transcum)
set(gcf, 'Position', [500, 200, 1000, 800])
xlabel('Time (years)')
ylabel('Total Energy Consumed (quintillions of BTUs)')
legend('Residential','Transportation','Location','northwest')
title('Cumulative US Energy Consumption from 1949 to 2016')
saveas(h,'figure_02.png')```

![Cumulative US Energy Use per Year from 1949-2016](./Problem 4/figure_02.png)

#Problem 5 (Freefall)

```g=figure();
hold on
timespan=30;

for h=[.1,1,5]
freefall(h,timespan)
end
set(0, 'defaultAxesFontSize', 16)
set(0,'defaultTextFontSize',14)
set(0,'defaultLineLineWidth',3)
set(gcf, 'Position', [200, 200, 1000, 800])
xlabel('Time (seconds)')
ylabel('Velocity (meters/second)')
legend('v analytical(0.1)','v numerical(0.1)','v analytical(1)','v numerical(1)','v analytical(5)','v numerical(5)','Location','southeast')
title('Velocity Comparison by Varying Time Steps')

saveas(g,'figure01.png')```

![Velocity Comparison by Varying Time Steps](./Problem 5/figure01.png)

#Problem 6 (Velocity and Acceleration)

#3D Velocity

```function [vx,vy,vz] = my_velocity(x,y,z,t)
% Help documentation of "my_velocity"
% This function computes the velocity in the x- and y-directions given
% three vectors of position in x- and y-directions as a function of time
% x = x-position
% y = y-position
% z = z-position
% t = time
% output
% vx = velocity in x-direction
% vy = velocity in y-direction
% vz = velocity in z-direction

vx=zeros(length(t),1);
vy=zeros(length(t),1);
vz=zeros(length(t),1);

vx(1:end-1) = diff(x)./diff(t); % calculate vx as delta x/delta t
vy(1:end-1) = diff(y)./diff(t); % calculate vy as delta y/delta t
vz(1:end-1) = diff(z)./diff(t); % calculate vy as delta y/delta t

vx(end) = vx(end-1);
vy(end) = vy(end-1);
vz(end) = vz(end-1);

end```

#3D Acceleration

```function [ax,ay,az]=my_acceleration(x,y,z,t)
% Help documentation of "my_acceleration"
% This function computes the acceleration in the x- and y-directions given
% three vectors of position in x- and y-directions as a function of time
% x = x-position
% y = y-position
% z = z-position
% t = time
% output
% ax = acceleration in x-direction
% ay = acceleration in y-direction
% az = acceleration in z-direction

function v=diff_match_dims(x,t)
v=zeros(length(t),1);
v(1:end-1)=diff(x)./diff(t);
v(end)=v(end-1);
end

[vx,vy,vz]=my_velocity(x,y,z,t);

ax = diff_match_dims(vx',t);
ay = diff_match_dims(vy',t);
az = diff_match_dims(vz',t);
%added apostrophe for derivatives of velocity

end```
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