Transverse vibrations of a thin loaded rod: theory and experiment

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.