Mass lumping techniques are widely used in structural dynamics to enhance the efficiency of explicit time integration schemes and to increase their critical time step, which is constrained by the largest discrete frequency of the system. For immersogeometric methods, Leidinger [1] first showed that under mild conditions on the spline’s order and smoothness, the largest frequency was not affected by small trimmed elements if the mass matrix was lumped. This finding was later supported by independent numerical studies. This talk presents a theoretical investigation of this property. By combining linear algebra and functional analysis, we derive sharp lower and upper bounds on the largest generalized eigenvalue for lumped mass approximations. These bounds not only provide practical estimates for critical time step sizes but also reveal the behavior of the largest eigenvalue for trimmed geometries. Our results confirm that smoothness is responsible for the boundedness of the largest eigenvalue as trimmed elements become smaller. However, our analysis also uncovers that while the largest eigenvalue remains bounded, the smallest eigenvalue tends to zero at least polynomially, with a rate depending on the degree and on the trimming configuration. This behavior may introduce spurious eigenvalues and modes in the low-frequency spectrum, analogous to those observed in the high-frequency spectrum for consistent mass approximations. The implications of these low-frequency spurious modes on transient simulations remain an open question and will be explored in future work. Numerical experiments in one- and two-dimensional settings validate our theoretical estimates, offering new insights into the interplay between trimming configurations and mass lumping in immersogeometric analysis. REFERENCES [1]L. Leidinger, Explicit isogeometric B-Rep analysis for nonlinear dynamic crash simulations,Ph.D. thesis, Technische Universität München (2020). [2] I. Bioli and Y. Voet, A theoretical study on the effect of mass lumping on the discrete frequencies in immersogeometric analysis. arXiv preprint (2024), arXiv:2410.17857.