Page 378 - MATLAB an introduction with applications

Direct Numerical Integration Methods ——— 363

v(:,i)=(X(:,i+1)–X(:,i–1)).*(1/(2*dt));
a(:,i)=(X(:,i+1)–2*X(:,i)+X(:,i–1)).*(1/dt^2);
end
end
t=[0:dt:T+dt];
plot(t,X(1,:),’–p’,t,X(2,:),’–*’);
xlabel(‘time(s)’);
ylabel(‘displacement(m)’);
legend(‘DOF-1’,’DOF-2',2);
grid on;

The output of the program is as follows:
time X(1) X(2)
0.000000 0.000000 0.000000
0.050000 -0.000000 0.001250
0.100000 0.000015 0.004998
0.150000 0.000067 0.011243
0.200000 0.000178 0.019981
0.250000 0.000376 0.031210
0.300000 0.000688 0.044924
0.350000 0.001142 0.061120
0.400000 0.001762 0.079793
0.450000 0.002571 0.100937
0.500000 0.003586 0.124545
0.550000 0.004821 0.150611
0.600000 0.006281 0.179128
0.650000 0.007969 0.210088
0.700000 0.009880 0.243481
0.750000 0.012004 0.279301
0.800000 0.014325 0.317535
0.850000 0.016824 0.358176
0.900000 0.019481 0.401212
0.950000 0.022271 0.446631
1.000000 0.025170 0.494422