1. The problem statement, all variables and given/known data A particle of mass m is confined to a horizontal plane. It is elastically bound to its equilibrium position by an isotropic elastic force, F=mω^2r Where r is the displacement of the particle from equilibrium and ω is a real constant parameter. From Newton's law, we obtain the equation of motion: r'' + ω^2r = 0. In rect. coordinates r(t) = ix(t) + jy(t). Obtain expressions for x(t) and y(t). 2. Relevant equations 3. The attempt at a solution The x-component of force : Fx = -x(t)mω^2 = mx''(t) x''(t) + x(t)ω^2 = 0 The solution to this DE is x(t) = c1cos(ωt) + c2sin(ωt) Then I'll apply the initial conditions given in the problem to obtain the constants. Here's the part I'm unsure about When I solve the differential equation for the y component I get y(t) = a1cos(ωt) + a2sin(ωt). I'm thinking I have to multiply this by t so that the solutions are linearly independent: y(t) = a1*tcos(ωt) + a2*tsin(ωt). Is this correct?