Consider the simple mass$$spring system shown below, where gravity is directed

into the page:

The force applied to the mass is $()=6+$ sin$(100),$ where $>0$ is small. In other

words, the applied force is oscillating around $6$ N$.$ The force generated by the spring depends

nonlinearly on the position of the mass:

$$spring$()=3+2+1$

Suppose you were interested in the behaviour of this system as it oscillates around its

operating point, and you were going to study its dynamics using a linear model. Find the best

spring stiffness $$ to use in the model.