The general formulation of a determinate solution problem is deduced for the transverse vibrations
of a thin loaded rod. The vibration frequencies of a thin homogeneous rod carrying a concentrated
mass as a function of the load’s position and mass are exactly solved. The dynamic measurement
method of Young’s modulus of the rods is presented within this theory. Our measurements of Young’s
modulus in the dynamic method agree with those in the traditional bending method, therefore the
theory is verified by our experiments.