Shifting the origine of time in isotropic oscillator

[esradw]

I am really lost here :(

The equation of motion X(t)=Ax Cos(wt-delta(x))
Y(t)=Ay Cos(wt-delta(y))
by shifting the origine of time ( t'=t+to where I need to figure out what is appropriate for time to ) and ( Delta=Delta(y)-Delta(x) )
I am suposed to find X(t)=Ax Cos(wt) and Y(t)=Ay Cos(wt-Delta)

I wish I could give some of my work but I can't even start it right now since I cannot think of the appropriate time (to) for X , I know that it can not be 0 because then I come to the same point again.
anyhelp appreciated
thanks

 

[StatusX]

I think you mean for the argument of that last function you gave to be t'. What do you get when t'=0? Compare this to what you get with the original function at the same time as measured in t (ie, in terms of to).

 

[esradw]

Yes t to be t' but in the question itself says once you find the solution with t',convert it into t .
I thought I can give to= dx/w then my equation become for X=Ax Cos( wt'-(wto+Deltax)) and when I unpack it, X/Ax=Cos(wt')Cos(dx+Deltax)+Sinwt' Sin(dx+Deltax) that has to stay only X/Ax=Cos(wt') how to come to this conclution ? How to get red of Cos(dx+Deltax))+Sinwt' Sin(dx+Deltax) I don't know :((((((
any idea?

 

[esradw]

I figured it out

thanks again