The dynamics of slender systems in three dimensions (3D), such as household objects, monuments, obelisks, and sculptures, are highly nonlinear and complex. The current investigation examines the applicability of a recently evolved physical model (PM) with mass-eccentricity for base excitation normal to the plane of eccentricity. The PM is simulated, combining distinct subsystems maintaining proper kinematic conditions in the Simscape Multibody Library. The rigid block is supported at its four corners by four very small spheres. The virtual plane that follows the linear visco-elastic Kelvin model is used to simulate the contact interaction between the rigid base and the body. A comparison of the results obtained from the PM to those by numerically solving a complex set of analytical equations for asymmetric rigid blocks in 3D is found to be in good agreement. For unidirectional excitation normal to the plane of the eccentricity, it is remarkable to note that the residual displacement and rotation of a 3D mass-eccentric rigid block is non-zero as the excitation expires. However, such residual responses are essentially zero for symmetric systems indicating that the block returns to its initial state unless overturned. The overturning spectrum for an out-of-plane rigid block is constructed and compared with that for the symmetric block. The physical model (PM) can be used for general asymmetry and help view the motion for a deeper insight into the intricate dynamics.