In the above diagram, a mass $m (= 5 \text{ kg})$ is attached to a spring with spring constant $k = 85 \text{ N/m}.$ A vane, attached to the mass $m$ and immersed in a liquid, exerts a damping force $F_d$ with damping constant $b = 3 \text{ kg/s}$ which is proportional to the velocity $v$ of the vane and mass. Approximately how long does it take for the mechanical energy of the oscillator to drop to $\frac{1}{3}$ of its initial value?

Assume that the gravitational force is negligible relative to the damping force $F_d$ and the force exerted by the spring $F_s.$