A mass of 1.75 kg stretches a spring 0.09 $\displaystyle {m}$. The mass is in a medium that exerts a viscous resistance of 84 $\displaystyle {N}$ when the mass has a velocity of 4 $\displaystyle \frac{{m}}{{s}}$. The viscous resistance is proportional to the speed of the object.

Suppose the object is displaced an additional 0.03 $\displaystyle {m}$ and released.

Find an function to express the object's displacement from the spring's equilibrium position, in $\displaystyle {m}$ after $\displaystyle {t}$ seconds. Let positive displacements indicate a stretched spring, and use 9.8 $\displaystyle \frac{{m}}{{s}^{{2}}}$ as the acceleration due to gravity.

u(t) = Preview Question 6