The 15.0-kg double wheel with radius of gyration of 100 mm about O is connected to the spring of stiffness k = 460 N/m by a cord which is wrapped securely around the inner hub. If the wheel is released from rest on the incline with the spring stretched 310 mm, calculate the maximum velocity v_{max} of its center O during the ensuing motion[ [m/s]. The wheel rolls without slipping.

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?