The correct choice is (d) Mẍ+Kx=0

To explain I would say: After Finite Element discretization of a structure, the free vibrations equation can be expressed as Mẍ+Kx=0 where M and K are the mass and stiffness matrices of the structure; x and ẍ are the displacement and acceleration vectors respectively. In a free vibration analysis, the external load vector is zero.