Convert second order of diff. equations to first order

[Basem]

Homework Statement

I have this set of equation:
My''+Cy'+Ky=0 but C=0
M is a matrix consist of {(-m) (0)/( -1/12mb^2) (-1/12mb^3)}
and K is a matrix of {(-K1-K2) (-K2b)/ ((K1b-K2b)/(2)) (-K2b^2/2)}
and y is a coordinate system which is (x1,θ)
Now i have to convert these two equations of second order to first order and i really got lost since its two equations and using matrices.
We can stack y' and y into z
so the final equation will be : z'=Az
Can anybody guide me how to do it?

 

[John Park]

If M and K were just constants and y were a single variable, would you recognise the equation?

 

[Basem]

If M and K were just constants and y were a single variable, would you recognise the equation?

I didn't really get what u mean? what do you mean y is a single variable? its a coordinate system (x1,θ)

 

[John Park]

what do you mean y is a single variable? its a coordinate system (x1,θ)

I know that; that's what "if . . . y were" implies. I'm asking if you recognise the corresponding scalar equation with C=0, which is often solved by reducing it to first order.

 

[haruspex]

My''+Cy'+Ky=0 but C=0

Assuming M^-1K is invertible, you can diagonalise it as P^-1DP.
See if that gives you some clues.
@Basem, do you need more hints?