Question

The free fall of a light particle of mass m released from rest and moving with a velocity v is governed by: 

mv = mg - bv, v(0)=0 

where g=9.81 m/s² is the gravitational acceleration and b/m = 0.2 is the coefficient, of viscous damping. Write a MATLAB script that solves the initial value problem using EulerODE, with h = 0.05 and returns a table of the estimated solutions at 0, 0.2, 0.4, 0.6, 0.8, 1, as well as the exact values at these points.

Answer 1

clc
clear all
close all
format long
bm=0.2;
g=9.81;
f=@(t,v) g-bm*v;
[t,y]=eulerSystem(f,[0,1],0,0.2);
Time=t(:);
Velocity=y(:);
Exact=981/20 - (981*exp(-t/5))/20;
Exact=Exact(:)
table(Time,Velocity,Exact)
function [t,y]=eulerSystem(Func,Tspan,Y0,h)
t0=Tspan(1);
tf=Tspan(2);
N=(tf-t0)/h;
y=zeros(length(Y0),N+1);
y(:,1)=Y0;
t=t0:h:tf;
for i=1:N
y(:,i+1)=y(:,i)+h*Func(t(i),y(:,i));
end
end

- MATLAB R2018a HOME O X Pradeep PLOTS APPS EDITOR PUBLISH VIEW do E C . Search Documentation E B Bold Hyperlink Bulleted List Preformatted Text Numbered List E Code Image Display Latex INSERT BLOCK MARKUP Italic Inline Latex M Monospaced INSERT INLINE MARKUP Windows System32 Publish PUBLISH O ох googleLinks.m X HomeworkLib2.m x testc.m X ahk.m x nse_filt.m x + | III Save Section Section with Title FILE INSERT SECTION Da O: Current Folder Name 0409 1029 1033 1036 1040 1045 1046 1049 1055 3082 Advancedinstallers af-ZA am-et AppLocker appraiser Details Editor - C:\Users\PRADEEP KALRA Documents\MATLAB\saveee.m saveee.m x bisectionmethodbypradeep.m X eulerSystem.m x Exact=981/20 - (981*exp(-t/5))/20; Exact=Exact (:) table (Time, Velocity, Exact) function [t,y)=euler System (Func, Tspan, Yo, h), to=Tspan(1) tf=Tspan (2); N=(tf-to) /h; y=zeros (length (YO), N+1); y(:,1)=YO; t=t0:h:tf; for i=1:N | vl:,i+1)=y: i) +h Func(t(i),y : i)); end Lend Command Window Workspace Time Velocity Exact Name # ans bm Exact Value 6x3 table 0.2000 [0;1.9233;3.7711;5.546... @(t,v)g-bm*v 9.8100 [0,0.2000,0.4000,0.600... [0;0.2000;0.4000;0.600... [0;1.9620;3.8455;5.653... [0,1.9620,3.8455,5.653... 9 1.962 3.84552 5.6536992 7.389551232 9.05596918272 1.92327800957855 3.77114320973551 5.54655257902343 7.25234715120733 8.89125656152498 i Time Velocity Hy fx >> euler System In 24 Col 4 ENG 5:32 PM US 04/15/20 Type here to search W

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