1. The problem statement, all variables and given/known data I'm trying to solve a system of two second order linear differential equations with the ode45 function. It is a two degree of freedom problem with 2nd order derivatives of both variables, u and theta. I believe that's referred to as a "stiff matrix"). I'm very confident in the A and B matrices themselves, but not on the running of ode45. One of the two problems I'm having is the values in my y matrix. I'm just not sure what should be there. 1's have the same result as zeros. I know y is the dependent variable, I just don't understand what the function would want me to type there. What does its being zeros mean? What does its being ones mean? My second problem is that I only know how to give a step input of force (f). As far as I can tell, the force input will be 628 Newtons the entire time. I tried to say f=628 when t<=0.015, but there is no "t" in the ode45 function. I'd like to give it an impulse if I can. 2. Relevant equations My code so far is: u0 = [0 ; 0]; theta0 = [0 ; 0]; FUN = @FUNA; T = [0 10]; y0 = [u0 ; theta0]; [TT,YY] = ode45(FUN,T,y0); plot(TT,YY(:,3)); function dy = FUNA(t,y) %Constants of system M = 70-5.876; m = 5.876; a = (((0.05)^2)+((0.13)^2))^0.5; IG= 0.0233; k = 500; g = 9.81; N = 2; %number of degrees of freedom %Define sub matrices MM=[(M+m) m*a ; m*a (IG+(m*a^2))]; K =[ 0 0 ; 0 (k-m*g*a)]; C =[0 0 ; 0 d*a*a]; F =[1; 0]; MI= inv(MM); Z = zeros(N,N); I = eye(N); %Define matrices A = [ Z I ; -MI*K -MI*C]; B = [ zeros(N,1); (MI*F) ]; f = 628; y = [0; 0; 0; 0]; dy= A*y + B*f; 3. The attempt at a solution I'd like to split this into four single order differential equations, but the second order derivative of both variables seems to stop me. I've run this code and I actually get plots, but they are either flat lines or ramp functions, depending on which of the four outputs I choose. I'm sure it's my use of the y matrix that's beating me.