We present spin-injection experiments in a nonlocal spin transport device where spin is injected from a ferromagnetic FeCo electrode into a GaAs epilayer. The magnetization of the injection contact is switched by Oersted fields generated by alternating current pulses. This enables fast and offset-free measurements of nonlocal spin signals. Due to a negligible time-averaged electron spin polarization, dynamic nuclear polarization effects are small and Hanle curves measured down to T=3 K can be fit very accurately by drift-diffusion theory if a small constant Overhauser field BN=0.4 mT is accounted for.