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lahuxixi
lahuxixi is offline
#3
Feb26-12, 03:26 AM
P: 10
Ok,this is what i currently have:
After solving the first question, i know that:
x(t)=x(0)cos(sqrt(A^2/(2w^2)-1)*t)
I know that if A^2/(2w^2)-1 is less than 0, then it is unstable, otherwise it is stable
The period seems to be 2*pi/sqrt(A^2/(2w^2)-1)
But i don't know how to find the shape of the trajectory in the phase plane, from what i know, i have to insert the formula into Matlab to obtain the graph .
For the unstable case, find the growth rate of deviation(i don't know what the growth rate of deviation is and how to find it) from the equilibrium point and find the trajectory in the (X; X') phase plane.( please help me with this too)

2. Rewrite the equation x''=x(1+Asin(wt)) as a system of two rst order ODE's so that the Matlab programme ode45 could be used.
For this, i can split it into two part:
x'=y
y'=x(1+Asin(wt))
But i don't know how to create a function file for the right-hand-side of this system to be used by ode45 to solve it.