Effects of sinusoidal velocity oscillation on the ignition of nonpremixed counterflowing hydrogen against heated air were computationally investigated with detailed descriptions of chemistry and transport. Results show that ignition basically behaves quasi-steadily for low frequency oscillations in that transient ignition occurs once the instantaneous strain rate falls below the steady-state ignition strain rate. For ignitable systems subjected to high frequency oscillations, increasingly larger amplitudes are needed to effect ignition as the frequency increases. In particular, for sufficiently rapid oscillations the system may not have enough time to be ignited before the flow condition again becomes unfavorable for ignition, and as such with increasing frequency a system can persist beyond the regime in which steady-state solutions do not exist. Furthermore, the ignitability of the system for a given frequency of oscillation was found to depend on whether the excursion time over the favourable straining conditions is long enough as compared to the characteristic ignition delay. Based on the characteristic ignition delay determined from the study of impulsive velocity reduction, the critical amplitude in effecting transient ignition for a given frequency of oscillation can be determined when the excursion time is comparable with the characteristic ignition delay. It is also shown that, unlike flame extinction under velocity oscillation, for a given air jet temperature there exists a cut-off frequency beyond which transient ignition is not possible. The normalized, cut-off angular frequency was found to be larger than unity, at which the system no longer responds to the imposition of oscillation. Finally, it is demonstrated that for the conditions studied herein, relevant for the second explosion limit in homogeneous systems, ignition is caused by radical proliferation instead of thermal feedback. Implications of the present findings to turbulent ignition modeling within the "flamelet regime" are discussed.