A mass of 2 $\displaystyle {k}{g}$ is attached to the end of a spring whose restoring force is 180 $\displaystyle \frac{{N}}{{m}}$. The mass is in a medium that exerts a viscous resistance of 20 $\displaystyle {N}$ when the mass has a velocity of 2 $\displaystyle \frac{{m}}{{s}}$. The viscous resistance is proportional to the speed of the object.

Suppose the spring is stretched 0.04 $\displaystyle {m}$ beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of $\displaystyle {5}{\sin{{\left({2}{t}\right)}}}$ $\displaystyle {N}$ at time $\displaystyle {t}$ seconds.

Find an function to express the steady-state component of the object's displacement from the spring's natural position, in $\displaystyle {m}$ after $\displaystyle {t}$ seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.)

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