Mass spring system where springs have mass

AI Thread Summary
Modeling a spring system with mass involves understanding the potential energy and forces acting on the masses connected by the springs. The system is grounded at both ends, leading to a constraint where the total length of the springs remains constant. Effective mass concepts can help in simplifying the calculations, but the challenge lies in accurately compiling the kinetic energies and potential energies of the springs and masses. Applying Newton's laws is essential, and deriving the kinetic energy for the springs based on their mass per length is a good start. The discussion emphasizes the need for a systematic approach to combine these energies for a comprehensive model.
sleventh
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hello all,
Recently I have been attempting to model a spring system (see below) where the springs themselves will hold mass. I should know how to do this but i accept defeat, how do you model the potential energy or a force system on two masses connected to three springs? I have read about effective mass but i fail to fully understand. Thank you all for the celerity.
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[M1]
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/
[M2]
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/
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In this design the spring system is vertical and grounded on both ends. Many thanks!
 
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Just apply Newton's laws. If l1,l2,l3 are the lengths of the springs at a time t ,l1+l2+l3 =constant due to the grounding. Hence, you get two equations in two unknowns.
 
yes I've been doing that and also derived the kinetic energy for the springs (1/6 mv^2 because of the springs mass per length) but am having difficulty compiling the kinetic energies and potentials.
 

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