Question

Question 3: DC&M 7.3; however, numerically integrate to find the evolution of the knee angle, o, from time t = 0 to time t = 1 using ode45, do not report an analytical solution to the differential equation. Plot your results.

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc%clears screen
clear all%clears history
close all%closes all files
format long;
J=0.154;
g=9.81;
m=4;
wn=6.28;
L=0.34;
al=0.228;
f1=@(x) [al-x(1)/(2*sqrt(J*(m*g*L/2-x(2))));wn-sqrt(m*g*L/(2*J)-x(2)/J)];
x=fsolve(f1,[1,1]);
c=x(1);
T=x(2);
f=@(t,y) [y(2); -(2*c*y(2) - 2*T*y(1) + L*g*m*y(1)^2)/(2*J)];
[T,Y]=ode45(f,[0,1],[0,2*pi]);
plot(T,Y(:,1));
xlabel('Time');
ylabel('\theta(t)');

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Kindly revert for any queries

Thanks.