Answer Happy

The equilibrium positions θe​ for a SDOF system with generalised coordinate θ may be determined using the potential energy function V(θ) as follows: dθdV​∣∣​θe​​=0 For a SDOF system, the stability of a specific equilibrium position θe​ is assured if the following condition is satisfied: dθ2d2V​∣∣​θe​​>0. Now, using the above equilibrium and stability requirements, examine the stability for the present problem and determine the stability of each physically possible equilibrium position θe​. Address the following items: i. Develop an expression for the equilibrium configurations θe​. ii. For each of the physically possible equilibrium solutions: A. Determine a numerical value of θe​ or the transcendental equation containing θe​. B. Examine the stability of the configuration for the each value of θe​. C. Determine restrictions on the physical parameters m,L,M, and Kr​ that are necessary to ensure stability.