Consider a mass m attached to a spring, so it oscillates along the z-axis of a Cartesian coordinate system, moving along the world line z = a cos Ωt, y = x = 0. Use the quadrupole-moment formalism to compute the gravitational waves h₊(t , r , θ , ∅) and h_×(t , r , θ , ∅) emitted by this oscillator, with the polarization tensors chosen as in Eqs. (27.71a). Pattern your analysis after the computation of waves from a binary.

Equation 27.71a.

e+ =( - ), ( = ( ); = 12 > = 1 r sin 0 ap (27.71a)