State Space Form of Projectile EOM with Air Resistance

[stdtoast]

I have equations of motion for a projectile with air resistance: where $$q = [x; y]$$

$$m \ddot{q_1} = -k \dot{q_1}$$
$$m \ddot{q_2} = -k \dot{q_2} - mg$$

I need to convert it into state space form, with the state $$X = [q; \dot{q}]$$. I'm told state-space form is a first order vector ODE: $$\dot{X} = [\dot{q}; \ddot{q}] = f(X)$$

Now I'm confused. I can write my equations of motions in matrix form like: $$m\ddot{q} = -k \dot{q} - [0; mg]$$. Is writing this in state-space form like vectorizing it again? Also, is f(X) a matrix? It's hard for me to figure out the problem without understanding the notation...

 

[stdtoast]

Nevermind, got it. Was a lot easier than I thought.