The following model describes a mass supported by a nonlinear spring. The units are SI, so g = 9.81 m/s2.
5 = 5g - (900y + 1700y3)
Find the equilibrium position yr, obtain a linearized model using the equilibrium as the reference operating condition, and compute the oscillation frequency of the linearized model.
Find the free response of the linearized model in terms of x(t) = y(t) - yr, for the initial conditions: x(0) = 0.002 m and (0) = 0.005 m/s.