Answer Happy

Q20
PLEASE answer all parts of the question. PLEASE SHOW and clearlyEXPLAIN all parts of the question and HIGHLIGHT the final solution.If the answer is correct I will upvote!
As a spring ages, its spring "constant" decreases in value. One such model for a mass-spring system with an aging spring is given below. mx'' (t) + bx' (t) + kex(t) = 0 In this equation, m is the mass, b is the damping constant. k and n are positive constant, and x(t) is the displacement of the spring from its equilibrium position. Let m = 1 kg, b = 2 N-sec/m, k = 2 N/m, and n = 2 (sec)-1. The system is set in motion by displacing the mass 2 m from its equilibrium position and then releasing it (x(0) = 2, x'(0) = 0). Find the first four nonzero terms in a power series expansion about t=0 for the displacement. (Type an expression that includes all terms up to order 4.) (...)