A novel result is presented that relates the transmission zeros (TZ) of a multivariate system described in matrix second-order form to the constrained natural frequencies (poles) of the system itself. The constrained system defines autonomous and energetically isolated subsystems, whose eigenfrequencies are the TZ of the system. The result is valid for systems with colocated input-output devices, and can be extended to the non-colocated case under some more restrictive assumptions. Into the considered class of systems fall lumped parameters mechanical structures, whose finite element models (FEM) are particularly suited for the use of the proposed method.