% dX = getDerivs(t, X)
% Function to get the state derivatives for the 16.07 spring-mass example
% 16.07, Fall 2004
% Last updated September 7th, 2004
%
% x' = F(x): "state derivatives are a function of the current state"
%
% t: current time given by the integrator
% X: current state vector given by the integrator
% dX: vector of state derivatives
%
% The equation that we are solving is:
%
%    x_dot_dot + (k/m)x = (1/m)A sin(omega t)
%
% See springmass.m for a definition of the state vectors
%
% Parameters and inputs are hardcoded inside; while bad coding practice, it avoids
%   the whole "function calling function function with nested function"
%   nonsense that would otherwise be necessary
%   ( http://www.mathworks.com/access/helpdesk/help/techdoc/math/funfun18.html#942684 )
function dX = getDerivs(t, X)
    % system parameters
    k = 1;                      % spring constant [N/m]
    m = 1;                      % mass [kg]
    A = 1;                      % forcing amplitude [N]

    
    % unpack the state vector (follow the definition)
    x     = X(1);
    x_dot = X(2);
    
    % set up some forcing parameters based on the current time
    if(t < 100)
        omega = .1;
    elseif(t < 150)
        omega = 1;
    else
        omega = 1 + .1*(t - 150);
    end;
    
    % Newton's 2nd: calculate the acceleration on the mass
    x_dot_dot = (1/m)*A*sin(omega*t) - (k/m)*x;    
    
    
    % pack up the vector of state derivatives (follow the definition)
    dX = [ x_dot;               % mass velocity [m/s]
           x_dot_dot ];         % mass accel [m/s^2]