An object of mass 2 grams is attached to a vertical spring with spring constant 32 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, positivedownwards. Write y for y(t) and yp for y' (t).y" =Σ(b) Find r1, r2, roots of the characteristic polynomial of the equation above.r1, r2 =Σ(b) Find a set of real-valued fundamental solutions to the differential equation above.Y1 (t) =ΣY2(t) =Σ(c) At t = 0 the object is pulled down v2 cm and the released with an initial velocity upwards of 4/2 cm/sec. Find the amplitude A > 0 and thephase shift o E (-1, 7] of the subsequent movement.A =ΣΦΣ

(a) Given the spring constant is 32 gram.s-2 and the mass of the object 2 gram. From Hook’s law,…

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