# 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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