Question: 5. Consider the second order ODE + pi+ 23z =0, (1) for a constant p. For g =1 and p = 1: (a) Convert (1)

5. Consider the second order ODE + pi+ 23z =0, (1) for a constant p. For g =1 and p = 1: (a) Convert (1) into a system of ODEs. (b) Find all equilibrium points of the system. () Classify each equilibrium point and determine its stability by linearising the sys- tem. (d) Using your results, sketch the trajectories in the (z, y)-phase space. (7 marks]

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