Question: How to compare or perform phase portrait ( diff(theta(t) vs. theta)?

 d^2(x)/d(t^2) + sin(x)=0  (1)

d^2(x)/d(t^2) + x = 0 (2)

d^2(x)/d(t^2) + ( x - (x)^3/6) = 0 (3)

1) Compare the results of numerical simulations of (1), (2), (3) to see how closely the period of the periodic orbits relate.

a) Perform a phase portrait ( (x)'(t) vs. x ) analysis for (1), (2), and (3).

b) Consider the initial conditions x(0)= x0 and x'(0)=0. For what intervals of x0 do the periodic orbits of (2) and (3) closely resemble the periodic orbits of (1)? Plot graphs of the period as a function of x0 using 10-15 intitial values.

c) Consider x0 =0 and x'(0) = v0. What changes from part (b) above? 

Please. I need helps with this problem in Maple. Thank so much!

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