A force of 2 pound stretches a spring 1 foot. With one end held fixed, a mass weighing 8 pounds is attached to the other end. The system is submerged in a fluid that imparts a damping force numerically equal to 3/2 times the instantaneous velocity. Initially, the mass is displaced 6 inches above the equilibrium position and released with a downward velocity of 3 ft/s. Find the equation of motion.

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j