Numerical Methods for Engineers

Published by McGraw-Hill Science/Engineering/Math
ISBN 10: 0073401064
ISBN 13: 978-0-07340-106-5

Chapter 1 - Mathematical Modeling and Engineering Problem Solving - Problems - Page 24: 1.19c

Answer

The solution is in the following image:
1561823987

Work Step by Step

Calculate the exact values of $v$ and $x$ using equation $(1.10)$ and $\operatorname{Eq}(1)$ from part (a). Use the code below, written in GNU Octave to obtain the results and plot. please see the image below: ____________________________ now we continue the solution t=0:2:10; v(1)=0; x(1)=0; for k=2:6 v(k)=v(k-1)+(9.81-12.5/68.1 * v(k-1))*2; x(k)=x(k-1)+v(k-1)*2; end disp(v) %output 0.00000 19.62000 32.03736 39.89621 44.87003 48.01792 disp(x) %output 0.00000 0.00000 39.24000 103.31471 183.10714 272.84719 te=0:0.1:10; for k=1:101 xe(k)=9.81*68.1/12.5*(te(k)+68.1/12.5*exp(-12.5/68.1*te(k)))-9.81*68.1*68.1/(12.5*12.5); ve(k)=9.81*68.1/12.5*(1-exp(-12.5/68.1*te(k))); end plot(t,x) hold on plot(te,xe) xlabel('t') ylabel('x') hold off plot(t,v) hold on plot(te,ve) xlabel('t') ylabel('v')
Small 1561823987
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