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ME3255S2017/lecture_01/lecture_01.md
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# Freefall Model | |
## Octave solution (will run same on Matlab) | |
```octave | |
%plot --format svg | |
``` | |
```octave | |
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 | |
```octave | |
t=[0,2,4,6,8,10,12]' | |
``` | |
t = | |
0 | |
2 | |
4 | |
6 | |
8 | |
10 | |
12 | |
Define constants and analytical solution (meters-kilogram-sec) | |
```octave | |
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 | |
```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 | |
``` | |
v_numerical = | |
0.00000 | |
19.62000 | |
36.03213 | |
44.83284 | |
47.70298 | |
48.35986 | |
48.49089 | |
Display time, velocity (analytical) and velocity (numerical) | |
```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)'); | |
``` | |
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 | |
```octave | |
plot(t,v_analytical,'-',t,v_numerical,'o-') | |
``` | |
![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"> | |