This work presents an analytical approach to estimate the natural frequencies of an Euler-Bernoulli beam carrying a small mass with rotary inertia. By assuming unchanged mode shapes, a simplified frequency formula is derived and validated using the Dynamic Stiffness Method. The results show high accuracy for small mass and inertia values, and highlight how mass placement and rotary effects influence vibration behavior. The method also offers potential for structural health monitoring applications, such as crack detection.