Arectangular key was used in a pulley connected to a line shaft with a power of 7.46 kw at a speed of 1200 rpm. if the shearing stress of the shaft and key are 30 mpa and 240 mpa, respectively what is the length of the rectangular key if the width is one fourth that of the shaft diameter?

Suppose that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?