Savchenko Problem 3.9.26

The key is recognizing this as a two-mass oscillator problem where both the support's mass and the body's mass contribute to the system's inertia. Rather than treating the spring as massless, you must account for how the elastic support itself moves—only a fraction of its mass participates effectively in the oscillation. Set up the equation of motion using the reduced-mass concept or effective-mass approach: the spring constant $k$ acts between two inertial elements, and the resonant frequency $\omega$ depends on both masses combined. Solve for the unknown body mass by relating it to the given stiffness, support mass, and measured frequency.

The key is recognizing this as a two-mass oscillator problem where both the support's mass and the body's mass contribute to the system's inertia. Rather than treating the spring as massless, you must account for how the elastic support itself moves—only a fraction of its mass participates effectively in the oscillation. Set up the equation of motion using the reduced-mass concept or effective-mass approach: the spring constant $k$ acts between two inertial elements, and the resonant frequency $\omega$ depends on both masses combined. Solve for the unknown body mass by relating it to the given stiffness, support mass, and measured frequency.