The equation of free transverse vibration of beams with two sections o
f partially distributed mass is derived and its exact solution has bee
n obtained. Experimental data for a cantilever beam are given to verif
y the computational results. Using a cantilever beam as an example, so
me interesting features of changes of natural frequencies with mass le
ngth and position are described. The method finally generalized for th
e case of beams with multiple spans of distributed mass.