Problem Value: 10 point(s). Problem Score: 0%. Attempts Remaining: 25 attempts. Help Entering Answers See Example 2.2.7, in Section 2.2, in the MTH 235 Lecture Notes. (10 points) An object of mass 3 grams is attached to a vertical spring with spring constant 48 grams/sec. Neglect any friction with the air. (a) Find the differential equation y’ = f(y,y) satisfied by the function y, the displacement of the object from its equilibrium position, positive downwards. Write y for y(t) and yp for y’ (t). y’ = (b) Find 71, 72, roots of the characteristic polynomial of the equation above. ri,r2 = (b) Find a set of real-valued fundamental solutions to the differential equation above. yi(t) = y2(t) = (c) At t=0 the object is pulled up 3 cm and the released with an initial velocity downwards of 4 cm/sec. Find the amplitude A> 0 and the phase shift € (-7,7] of the subsequent movement. A= Σ φ =