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01_Introduction/.ipynb_checkpoints/lecture_01-Copy1-checkpoint.ipynb
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# Freefall Model | ||
## Octave solution (will run same on Matlab) | ||
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```octave | ||
%plot --format svg | ||
``` | ||
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```octave | ||
set (0, "defaultaxesfontname", "Helvetica") | ||
set (0, "defaultaxesfontsize", 18) | ||
set (0, "defaulttextfontname", "Helvetica") | ||
set (0, "defaulttextfontsize", 18) | ||
set (0, "defaultlinelinewidth", 4) | ||
``` | ||
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Define time from 0 to 12 seconds | ||
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```octave | ||
t=[0,2,4,6,8,10,12]' | ||
``` | ||
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t = | ||
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0 | ||
2 | ||
4 | ||
6 | ||
8 | ||
10 | ||
12 | ||
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Define constants and analytical solution (meters-kilogram-sec) | ||
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```octave | ||
c=0.25; m=60; g=9.81; v_terminal=sqrt(m*g/c); | ||
v_analytical = v_terminal*tanh(g*t/v_terminal) | ||
``` | ||
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v_analytical = | ||
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0.00000 | ||
18.61630 | ||
32.45521 | ||
40.64183 | ||
44.84646 | ||
46.84974 | ||
47.77002 | ||
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```octave | ||
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 | ||
``` | ||
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v_numerical = | ||
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0.00000 | ||
19.62000 | ||
36.03213 | ||
44.83284 | ||
47.70298 | ||
48.35986 | ||
48.49089 | ||
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Display time, velocity (analytical) and velocity (numerical) | ||
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```octave | ||
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)'); | ||
``` | ||
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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 | ||
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```octave | ||
plot(t,v_analytical,'-',t,v_numerical,'o-') | ||
``` | ||
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![plot of | ||
velocities](https://github.uconn.edu/rcc02007/ME3255S2017/blob/master/lecture_01/output_10_0.svg) | ||
<img | ||
src="https://github.uconn.edu/rcc02007/ME3255S2017/blob/master/lecture_01/output_10_0.svg"> | ||
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