s(x,y)=Asinwt i + 3Asin3wt j

What is its time period? Also find the expression for total mechanical energy wrt time.

I tried it in the following way

V=Awcoswt i + 3Awcos3wt j = Aw[(coswt)^2 +9(cos3wt)^2]^(1/2)

KE=0.5m(Aw)^2[(coswt)^2 +9(cos3wt)^2]

a= -[A(w^2){sinwt i + 9sin3wt j }]

F=ma

PE=F.s = -m[(Aw)^2{(sinwt)^2 + 27(sin3wt)^2}]

Total energy=KE + PE

= m(Aw)^2[0.5{(coswt)^2 +9(cos3wt)^2}- {(sinwt)^2 + 27(sin3wt)^2}]

Is this correct? And how to calculate the time period?