A charged particle produces an electric field E(r, t) as it passes by an isolated atom. Model

Question:

A charged particle produces an electric field E(r, t) as it passes by an isolated atom. Model a bound electron in the atom as a damped harmonic oscillator with natural frequency ω₀ and damping constant Γ". Assume that the electric field induces small-amplitude, nonrelativistic motion of the bound electron near the origin of coordinates. If Ê(ω) is the Fourier transform of E(r = 0, t), show that the energy transferred to the bound electron from the field is