Astudent sits on a rotating stool holding two 2.8-kg objects. when his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. the moment of inertia of the student plus stool is 3.0 kg · m2 and is assumed to be constant. the student then pulls in the objects horizontally to 0.34 m from the rotation axis. (a) find the new angular speed of the student.

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?