blah

Problem 3/freefall.m → Problem 5/freefall.m

@@ -1,23 +1,23 @@
-function [v_analytical,v_terminal,t]=freefall(h,timespan)
-    % help file for freefall.m
-    % N is number of timesteps between 0 and 12 sec
-    % v_an...
-    N=timespan/h+1;
-    t=linspace(0,timespan,N)';
-    c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c);
-
-    v_analytical = v_terminal*tanh(g*t/v_terminal);
-    v_numerical=zeros(length(t),1);
-    delta_time =diff(t);
-    for i=1:length(t)-1
-        v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*delta_time(i);
-    end
-    % Print values near 0,2,4,6,8,10,12 seconds
-    indices = round(linspace(1,length(t),7));
-    fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\n')
-    fprintf('-----------------------------------------------\n')
-    M=[t(indices),v_analytical(indices),v_numerical(indices)];
-    fprintf('%7.1f | %18.2f | %15.2f\n',M(:,1:3)');
-    plot(t,v_analytical,'-',t,v_numerical,'o-')
-end
-
+function [v_analytical,v_terminal,t]=freefall(h,timespan)
+    % help file for freefall.m
+    % N is number of timesteps between 0 and 12 sec
+    % v_an...
+    N=timespan/h+1;
+    t=linspace(0,timespan,N)';
+    c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c);
+
+    v_analytical = v_terminal*tanh(g*t/v_terminal);
+    v_numerical=zeros(length(t),1);
+    delta_time =diff(t);
+    for i=1:length(t)-1
+        v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*delta_time(i);
+    end
+    % Print values near 0,2,4,6,8,10,12 seconds
+    indices = round(linspace(1,length(t),7));
+    fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\n')
+    fprintf('-----------------------------------------------\n')
+    M=[t(indices),v_analytical(indices),v_numerical(indices)];
+    fprintf('%7.1f | %18.2f | %15.2f\n',M(:,1:3)');
+    plot(t,v_analytical,'-',t,v_numerical,'o-')
+end
+

Problem 3/freefall_2.m → Problem 5/freefall_2.m

@@ -1,6 +1,6 @@
-figure
-hold on
-timespan=30;
-for h=[.1,1,5]
-    freefall(h,timespan)
-end
+figure
+hold on
+timespan=30;
+for h=[.1,1,5]
+    freefall(h,timespan)
+end

Problem 3/freefall_comparison.m → Problem 5/freefall_comparison.m

@@ -1,17 +1,17 @@
-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')
+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')

Problem 5/my_acceleration.m → Problem 6/my_acceleration.m

@@ -1,27 +1,27 @@
-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
+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

Problem 5/my_velocity.m → Problem 6/my_velocity.m

@@ -1,27 +1,27 @@
-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
-
+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
+