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Magical the behavoiur of the solution of d^2x/dt^2+adx/dt+4x
depends on the value of a
Note a=alpha
a)find the ranges of a so that the solution displays
i)overdamping
ii)critical damping
iii)underdamping(decaying oscilations)
iv)growing oscilations
v)constant oscilations
b)For each of these cases, choose value of a within your stated
ranges, and find the general solution, displaying your solution
pictorially to show the behaviour of the solution
c) By carefully considering all the possible values of a identify the ranes which do not lead to the behavouirs listed in a, and describe the typical behaviour in this case