A golf player hits a 0.045\, \text {kg}0.045kg0, point, 045, start text, k, g, end text golfball that is initially at rest, changing its momentum by 4.2\, \dfrac {\text{kg}\cdot \text m}{\text s}4.2 s kg⋅m 4, point, 2, start fraction, start text, k, g, end text, dot, start text, m, end text, divided by, start text, s, end text, end fraction.

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?