The position of a certain undamped spring-mass system satisfies the initial value problem for u(t)):-y^{\prime \prime}+\frac{1}{4} y^{\prime}+2 y=0 ; \quad y(0)=0 ; y^{\prime}(0)=2-(a) Find the solution of this initial value problem. Show all detailed steps.-(b) Plot (using MATLAB) y versus t and y versus t on the same plot. Clearly label you rplots and clearly identify the lines for each curve.-(c) Plot y' versus y; that is, plot y(t) and y (t) parametrically with t as parameter. This plot is called the phase plot and the y-y plane is called the phase plane.-(d) Observe that a closed curve in the phase plane corresponds to a periodic solution y(t).What is the direction of motion on the phase plot as t increases (i.e. clockwise or anti-clockwise)?

Advanced Mathematics(Mathematics)

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