Q1:

> Regarding last question in lab2 (particle motion), I'm not sure what do
> you mean to plot xy-displacement as parameter of time? Do u mean plotting
> x vs. time and y vs. time in each subplot and repeat that for each
> different alpha or is it sufficient to plot x position vs. y position? I
> am not sure how to plot in 3D for this problem.
 
A1:

You should plot y versus x,  NOT y(t) or x(t).
3D plotting is not necessary here!

Q2: 

> In the problem 2 (Motion of a particle), we have a system of equations with
> x,x' and x'', the same with y. I first wanted to introduce the vector [x x']
> as we did in the first lab, but as the system is nonlinear, we cannot write
> the right member in the form "Ax". Moreover, we have to solve in the same
> time the problem with X and with Y. Should we write a new vector [x x' y y']
> and linearize the problem to solve it or is there a way to solve exactly the
> problem without linearization ?

A2:

You should introduce a vector u=(u1,u2,u3,u4)^T, 
where u1=x, u2=x', u3=y, u4=y' then write the system in the form
u'=f(t,u), u(0)=u0.
The system is nonlinear and must be kept so!
Linearization must not be done and is not
necessary, since numerical methods for the IVP
can handle nonlinear systems!!