where m is the attached mass. In this calculation we have neglected the mass of the beam. Hence it may be observed that by considering a point mass at the tip we obtained one natural frequency of the system. Instead of modeling this system as a single-spring mass if one consider the beam to be consist of several masses, then the system can be modeled as a multi-degree of freedom system as shown in figure 10.2(a). But as the dimension of each elemental mass considered in the above case is arbitrary, one may consider the beam as a continuous system with infinite number of distributed mass and stiffness and hence has infinite number of natural frequencies as shown in fig 10.2 (b).

Fig. 10.2(a,b) Multidegree Freedom System