Amass weighing stretches a spring . the mass is attached to a viscous damper with a damping constant of . if the mass is set in motion from its equilibrium position with a downward velocity of , find its position at any time . assume the acceleration of gravity .

When a vertical beam of light passes through a transparent medium, the rate at which its intensity i decreases is proportional to i(t), where t represents the thickness of the medium (in feet). in clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity i0 of the incident beam. what is the intensity of the beam "10" feet below the surface? (give your answer in terms of i0. round any constants or coefficients to five decimal places.)