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, positive downwards. 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) = Σ Y2(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 the phase shift o E (-1, 7] of the subsequent movement. A = ΣΦ Σ

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, positive downwards. 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) = Σ Y2(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 the phase shift o E (-1, 7] of the subsequent movement. A = ΣΦ Σ