
using initial conditions
i cant see how they got X and Y expressions
V_x is the derivative of X(t) by t
'A' and phi are needed to be found
but when i dont know how to innpur the initial condition to find A_x and A_y
because when we integrate x' expression bot sides i get
x(t)x(0)=[A_x*cos(wt+phi)]/w  [A_x*cos(0+phi)]/w
so i cant put 'b' instead of x(0) but it doesnt give me A_x parameter value
http://i56.tinypic.com/deb2xl.jpg

if you are confuswsed with the simbols thev
v_x=x(t)'
v_y=y(t)'
tell me if you cant understand some simbol translation
its all differential equations

To my opinion $\displaystyle w_c $ in not correct.
And y(t) not satisfies initial contition.
At first you must get final expressions of $\displaystyle v_x, \ v_y$ and
then integrate using initial contitions $\displaystyle x(0), \ y(0).$.
There are 4 unknown variables in $\displaystyle v_x, \ v_y$ and
from initial conditions are 2 given. Additional may be obtained
from conservation laws.