A parsimonious mass–spring system capable of being tuned for arbitrary repeated natural frequencies

The case of repeated natural frequencies occurring is very important in vibration analysis, which occurs more frequently in a complex system. However, the few degree-of-freedom systems (especially the mass–spring systems) possessing repeated natural frequencies are rare in literature. A parsimonious mass–spring system is constructed. By tuning the system physical parameters, the mass and spring coefficients, any type of repeated natural frequency can be produced. This model is instantiated by cases of three and four degree-of-freedom systems.