EQUILIBRIUM POINTS OF TWO MASSES CONNECTED BY A SPRING OF VARIABLE STIFFNESS AND DAMPING COOEFICIENTS

ABSTRACT This work is aimed to study of this work is study the dynamics of two masses connected by a spring of variable stiffness and variable dapping coefficients in between them, both masses are externally excited and are attached different springs and dampers, the equilibrium points (EPs) for the driven mass m1is found to be highly dependent on stiffness of the connecting spring, it is found that for small coupling stiffness nine equilibrium points are seen for the mass m1 while three EPs are seen for the mass m2, for intermediate coupling five EPs are seen for mass m1 while the EPs of the of m1 remain at three, while for strong connecting stiffness the EPs of the two masses m1 and m2 have three EPs. The stabilities of these EPs are evaluated by obtaining the eigenvalues of Jacobian, the eigenvalues show that all the EPs are stable for damping coefficient values ranging 0 – 2. Keywords: Equilibrium, Masses, Spring, Damping, Jacobian