Consider a forced single degree-of-freedom system governed by

mẍ(t) + 2ζωẋ(t) + ω²x(t) = ω² cos(ωt),

where ζ and ω are the damping ratio and undamped natural frequency of the system, respectively, while ω_f is the forcing frequency. The amplitude of the forced steady state response of this system is given by [ (1 - r²)² + (2ζr)² ]^-1/2, where r = ω_f/ω. The peak amplitude of this response occurs at a frequency ω_f = ω√(1 - 2ζ²). If ω_d denotes the damped natural frequency of this system, which one of the following options is true?