You need to calculate the mass matrix as well. With it and the stiffness matrix you can form the dynamical matrix and either extract its eigenvalues (reciprocal of the squared angular eigenfrequencies) or use vector iteration to find the modes first and from them the eigenvalues.
You can obtain the dynamical matrix (D = inv[M].[K]) from the stiffness [K] and mass matrix [M]. The eigen values and eigen vecors of [D] correspond to the mode shapes and square of modal frequencies of the system respectively.