## Bending Moment in Pendulum with Spring

## Bending Moment in Pendulum with Spring

(OP)

I'm not sure of the best forum to post this question, so I thought I would try here. I have a pendulum with a spring attached. I can determine a relationship to predict the natural frequency of the system. Where I'm having trouble is finding a relationship to predict the maximum bending moment in the beam, so that I size the beam properly. I've attached an illustration. Any help would be appreciated.

## RE: Bending Moment in Pendulum with Spring

For a rigid beam, the natural frequency is

omega = sqrt[(kh²+mgz)/(mz²)]

The equation of motion then becomes

theta = A*sin(omega*t) where A is the (arbitrary) amplitude of the motion.

Double-differentiate to get accelerations.

From here it is a simple exercise to employ d'Alembert's Principle to derive an algebraic expression for the bending moment you are seeking.

## RE: Bending Moment in Pendulum with Spring

Structural Engineering Otherforum, where it has had numerous replies. See thread507-380631: Bending moment in a Pendulum with Spring.Grrrr!