Application of some stability criteria of stability for the spring equation

الملخص EN

This study aimed to investigate the stability of the equation for energy motion of spring using two criteria, namely routh_hurwitz and mikailove, and compare between them.

discuss one of the physical applications of the differential equation, which is the issue of the spiral spring and its waning and non-diminishing vibrations.

study its stability by imposing certain conditions so that we get a second-order equation and homogeneous.obtianin stability the diminishing vibratory motion of the spring is conserving energy and stability the differential equation motion for spring as well as the diminishing vibratory motion of the spring is not conserving energy in the first criterion and instability the diminishing vibratory motion of the spring is conserving energy for tow cases in the second.