Amass weighing 4 lb stretches a spring 1.5 in. the mass is given a positive displacement of 2 in from its equilibrium position and released with no initial velocity. assuming that there is no damping and that the mass is acted on by an external force of 2 cos 3t lb, formulate the initial value problem describing the motion of the mass. (a computer algebra system is recommended.)

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