Industrial processes often require the damping of vibrations. Consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of k = 59800 N/m. This workbench is used when creating products that involve highly unstable chemicals. According to specications, the acceleration of the manufacturing equipment must be held to less Macmillan Learning than 20.9 mst for the manufacturing process to proceed safely. The amplitudes of vibrations are expected to remain under E 13' 0.472 mm throughout. Given that the workbench and maufacturing equipment have a combined mass of m = 6.15 kg, nd the maximum acceleration amx expected of the equipment and workbench. Ignore the mass of the springs. "J Does the workbench meet the specications for acceleration? 0 no 0 yes An engineer decides to damp the oscillations by applying one shock absorber to each spring. These shock absorbers apply a velocitydependent drag force 1:\" = b3 that opposes the motion of the bench. For proper damping, the engineer decides that the motion of the bench should drop to halfamplitude within 0.36? s. In other words, within 0.36? s, the amplitude of motion should drop by a factor of one half. When purchasing shock absorbers, what damping coefcient 5 should the engineer specify to the industrial equipment supplier? Assume that the oscillations are underdamped