function second_oder_ode
h=0.01;
t = 0:h:60;
initial_y = 0;
initial_dydt = 0;
[t,y]=ode45( @rhs, t, [initial_y initial_dydt] );
plot(t,y(:,1));
xlabel('t'); ylabel('y');
function y_out=rhs(y)
L0=128;
W=100;
g = 9.81;
A=(pi*(0.02)^2)/4;
m=W/g;
if y(1)<=L0
y_out = [y(2);g];
else
y_out = [y(2);g-((Viscosity(y)*(y(1)-L0)^0.8)*y(2))/(m*y(1))-(ElasticModulus(y)*y(1)*A)/(m*L0)];
end
function [eta]=Viscosity(y)
L0=128;
gammadot= y(2)/(y(1)-L0);
table_gammadot=[0.02 0.05 0.09 0.18 0.3 0.5 0.9 1.8 3 5 9 18 30];
table_eta=[62.20241 28.73309 16.96822 9.024566 5.742004 3.634656 2.099485 1.107372 0.703221 0.429745 0.251424 0.134518 0.082058];
eta=interp1(table_gammadot, table_eta, gammadot, 'nearest', 'extrap');
end
function [G]=ElasticModulus(y)
L0=128;
lambda=y(1)/L0;
table_lambda=[1.355667 1.67225 1.981016 2.309324 2.645449 2.973758 3.302066 3.626466 3.954774 4.294807 4.619207 4.947515 5.291457 5.486879 5.93244 6.25684 6.596873 6.925181 7.241764];
table_G=[117.957 177.1892 183.9973 189.4069 193.7871 196.9072 195.846 199.0777 205.7417 168.6455 175.6384 234.3298 252.4299 277.298 291.751 317.9678 347.2071 382.3623 478.0037];
G=interp1(table_lambda, table_G, lambda, 'nearest', 'extrap')*1000;
end
end
end