A linear elastic spring is suspended on two extremes and it will stretch under its weight. How can I write down the differential equation for the the equilibrium configuration? And the exact PDE of the oscillations?
Thank you in advance
The equation of equilibrium can be obtained by using the calculus of variation.The Eulers equation will give the solution where effect of elasticity to be considered.
As presented, I think that the equation is an ODE (not a PDE). Could you please join a figure in order to be sure I understood the problem you want to treat ? Thank you.
Is this the problem of an vibrating string (for the oscillations, an PDE) and the catenary (for the equilibrium, an ODE)?
Try to refer to the paper
A Closed-Form Refined Model of the Cables' Nonlinear Response in Cable-Stayed Structures
by myself. Also, there you can find some references for dynamical case. Let me know
- Badges
- Science topic
- Similar topics
- Mathematics
- Applied Mathematics