Decay Time of Damped Oscillator

Classical Mechanics Level pending

A \(10 \text{ kg}\) mass is attached to a spring of spring constant \(10 \text{ N}/\text{m}\). The entire system is submerged in water, which exerts a viscous damping force on the mass \(F_d = -(2 \text{ N}\cdot \text{s}/\text{m}) \:v\). The mass is pulled so that the spring is displaced from equilibrium by \(.1 \text{ m}\) and is released. Find the \(1/e\) decay time of oscillation in seconds.

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