Derive the set of differential equations for a three mass-four spring system (Figure) that describes their time

Question:

Derive the set of differential equations for a three mass-four spring system (Figure) that describes their time motion. Write the three differential equations in matrix from,

[Acceleration vector] + [k/m matrix][displacement vector x] = 0

Note each equation has been divided by the mass. Solve for the eigenvalues and natural frequencies for the following values of mass and spring constants: k1 = k4 = 15 N/m, k2 = k3 = 35 N/m, and m1 = m2= m3 = 1.5kg.