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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

I'm a bit confused.  The text on your diagram states that the beam is NOT rigid, but the diagram itself implies that it IS rigid.  If you have derived a formula for the natural frequency you must have assumed a rigid beam, because it's too hard if the beam is flexible.

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.

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