Code

close all
clear all
clc

h=.01;
t = [0:h:8];
v = (sqrt(9.81./6.89)).*((1+exp(2.*6.89.*t))./(1-exp(2.*6.89.*t)));
plot (t,v)
xlim([0 10])
ylim([-0.4 0.8])

%RK2 Method
v(1) = 0;
v2(1) = 0;
for i = 1:1:length(t)-1
    k11 = v(i); %k1 for x1
    k12 = v(i) + h.*k11; %k2 for x1
    v(i+1) = v(i) + h.*(0.5.*k11 + 0.5.*k12); %calculate next x1 value
    k21 =(sqrt(9.81./6.89)).*((1+exp(2.*6.89.*t))./(1-exp(2.*6.89.*t))).*(v(i)); %k1 for x2
    k22 =(sqrt(9.81./6.89)).*((1+exp(2.*6.89.*t))./(1-exp(2.*6.89.*t))).*(v(i)+h.*k21); %k2 for x2
    v2(i+1) = v(i)+ h.*(k21+k22); %calculate next x2 value
end