1. The problem statement, all variables and given/known data A particle of mass m is subjected to an isotropic, two dimensional, harmonic central force, F=-kr. (r=(x,y)). At t=0 the particle is at r=A and has velocity V yhat. Find r' r'' θ' θ'' in 2D spherical polar coordinates. 2. Relevant equations Fx=-kx Fy=-ky 3. The attempt at a solution I have found the equations of motion, as well as the particular solutions using the initial conditions. So far I have: x(t)=-Acos(wt-π) y(t)=V/wcos(wt-π/2) From here I found r' to be Awsin(wt-π)-Vsin(wt-π/2) and r'': Aw2cos(wt-π)-Vwcos(wt-π/2) Im fairly certain everything up to this point is correct, but I have no idea what to do about theta. I know in spherical polar coordinates θ=arctan(y/x) but I don't think I can just take the derivative in this form. I have tried setting x(t)=-Acos(wt) and y(t)=V/wsin(wt) by using the relation between sines and cosines offset by pi/2.This has brought me to θ=arctan((V/wa)tan(wt)). Again, I hit a wall with finding the derivatives.