I am trying to estimate the damping ratio of steel in bending. I have a situation where I need to know the dynamic response of an inverted pendulum. A picture is worth a thousand words, so here you go: The vibration will be free; it is caused be the initial position of the system. I can calculate the stiffness of the flexural steel based on the length, cross section, and material properties. The problem is estimating the damping. I want to know how long it takes the ocsillations to die down to a specified level. I have done some research on google and so far I have only been able to find lengthy thesis full of differential equations and no real applicable conclusions. I am aware of the logarithmic decrement method, but I do not have the luxury of setting up a full scale model. What I am looking for is some sort of relation between the geometry and the material properties to estimate the damping. Can someone point me in the right direction? Thank you!