Consider the given initial value problem: y"+ 4y' + 4y = 0, y(0) = 1, y'(0) = (A) Explain why the IVP can represent a mass-spring system. In your explanation,

you need to describe all the system's attributesincluding initial displacement and initial velocity. (B) Classify the mass-spring system using all the terms we've learned so far. (C) Find the system's damping coefficient and spring constant. O) Is there any external force on the system? Explain why or why not. (E) Use the answers from (A) to (D) above to sketch all the possible graphs of the solution. [Do not use an analytic solution of the differential equation to answer this question.] (F) Solve the IVP. (G) Find the limit as t + 0 of the solution you found in (F) above.(solution) Use algebra to determine how many zeros of the solution you found in (F) has. ) Use calculus to determine how many local extrema the solution you found in (F) has. J) Find the maximum displacement. (K) Sketch the solution curve using all the facts about the IVP and its solution. On your sketch, you need to include proper labels for all the special values/points of the curve you found above. (L)-(M) The system has an external force of 12te-2", so the non-free mass-spring system is described by y" + 4y' + 4y = 12te-2",y(0) = 1, y'(0) = 0. (L) Find a particular solution of the nonhomogeneous differential equation using the following method. (i) Method of Undetermined Coefficientsn) i) Method of Variation of Parameters Find the particular solution of the IVP.