Hi, friend! The ode you provided is a 2nd order ode. Follow the code you will know how to solve this ode. But at first, since both the mass m and the stiffness K is positive, the equation should be modified as:
Then the code is
% Firstly, define the ode function
% Here we set x(1)=x and x(2)=x';
% Then odefun = [x'; x''] = [x(2); -K/m*x*(1)+g]
odefun = @(t,x, K, m, g)[x(2); -K/m*x(1)+g];
K = 1; % set stiffness
m = 1; % set mass
g = 10; % set gravity
x0 = [0;0]; % set the initial conditions [initial position and initial velocity]
tspan = 0:0.1:20; % set t span
[t, x] = ode45(@(t,x)odefun(t, x, K, m, g), tspan, x0); % solve with ode45
plot(t,x(:,1),'r-') % plot results
hold on
plot(t,x(:,2),'b-')
xlabel('t'); ylabel('x or dx/dt')
legend('x','dx/dt')
