Top: example displacement ξ(t) using Eq. (6) as a function of time, which satisfies condition (7). The amplitudes are a₀ = 2 Mm and a₁ = 4 Mm. The two oscillations are in phase. The grey curve shows the impulsive part. The red line is the fitted damped oscillation (1). Bottom: τγ as a function of the ratio of amplitudes a₀/a₁ for different phase differences between the two solutions in Eq. (6). Here a₀ represents the full amplitude of the driven oscillation (including the square-root denominator). We assumed ω₀ = 2π/250 rad s^-1, ω = 2π/200 rad s^-1, γ = 1/530 Hz.