1. The problem statement, all variables and given/known data We have a rod of length L fixed to a rigid support. At the end of the rod there is a mass, m. Assume that the rod has no mass. Find the first natural frequency for the bending, axial and torsion modes. 2. Relevant equations 3. The attempt at a solution So I'm reviewing some stuff from my undergraduate degree as I will be taking night classes for my master's in systems and controls next year. I'm doing some very basic stuff but wowzie is it difficult to remember some of this stuff that I haven't seen since I graduated. So lets take the first part, that I think that I remember. For bending you can set up the problem as mx'' = kx - mg This is of a familiar form and we can see that for a simple mass-spring system the natural frequency is Wn=sqrt(k/m) So for a 1 DOF system we have found the 1st natural frequency. Is this correct? I'm not sure what they mean by the axial one. Would I simply assume that the rod is acting as a spring and that the mass m is pushing down on it? And for the torsional one would I just adjust my k to be the torsional value, but where does the supposed torque come from?