An 8-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. assume that the spring constant is 40 n/m and the damping constant is 4 n-sec/m. at time =0, an external force of =4cos(+) is applied to the system. formulate the initial value problem describing the motion of the mass and determine the amplitude and period of the steady-state solution.

An athlete swings a ball, connected to the end of a chain, in a horizontal circle. the athlete is able to rotate the ball at the rate of 8.13 rev/s when the length of the chain is 0.600 m. when he increases the length to 0.900 m, he is able to rotate the ball only 6.04 rev/s. (a) which rate of rotation gives the greater speed for the ball? 6.04 rev/s 8.13 rev/s (b) what is the centripetal acceleration of the ball at 8.13 rev/s? m/s2 (c) what is the centripetal acceleration at 6.04 rev/s? m/s2