lecture_01.md

Freefall Model

Octave solution (will run same on Matlab)

%plot --format svg

set (0, "defaultaxesfontname", "Helvetica")
set (0, "defaultaxesfontsize", 18)
set (0, "defaulttextfontname", "Helvetica")
set (0, "defaulttextfontsize", 18) 
set (0, "defaultlinelinewidth", 4)

Define time from 0 to 12 seconds

t=[0,2,4,6,8,10,12]'

t =

    0
    2
    4
    6
    8
   10
   12

Define constants and analytical solution (meters-kilogram-sec)

c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c);

v_analytical = v_terminal*tanh(g*t/v_terminal)

v_analytical =

    0.00000
   18.61630
   32.45521
   40.64183
   44.84646
   46.84974
   47.77002

v_numerical=zeros(length(t),1);
for i=1:length(t)-1
    v_numerical(i+1)=v_numerical(i)+(g-c/m*v_numerical(i)^2)*2;
end
v_numerical

v_numerical =

    0.00000
   19.62000
   36.03213
   44.83284
   47.70298
   48.35986
   48.49089

Display time, velocity (analytical) and velocity (numerical)

fprintf('time (s)|vel analytical (m/s)|vel numerical (m/s)\n')
fprintf('-----------------------------------------------')
M=[t,v_analytical,v_numerical];
fprintf('%7.1f | %18.2f | %15.2f\n',M(:,1:3)');

time (s)|vel analytical (m/s)|vel numerical (m/s)
-----------------------------------------------
    0.0 |               0.00 |            0.00
    2.0 |              18.62 |           19.62
    4.0 |              32.46 |           36.03
    6.0 |              40.64 |           44.83
    8.0 |              44.85 |           47.70
   10.0 |              46.85 |           48.36
   12.0 |              47.77 |           48.49

plot(t,v_analytical,'-',t,v_numerical,'o-')