Dimensionless frequency, ωτ_Ap, versus time in units of the internal Alfvén travel time, τ_Ap = L/v_Ap. Results corresponding to the fundamental mode and the lowest seven harmonics obtained by numerically solving Eq. (14) for a flowing thread with L_p/L =  0.1, v₀/v_Ap =  0.05, and z₀/L =  −0.25. The vertical dotted line denotes the time when the prominence thread is centered within the flux tube.