  Recently new approaches for sensing the frequency of time dependent
Hamiltonians have been presented, and it was shown that the optimal Fisher
information scales as $T^{4}.$ We present here our interpretation of this new
scaling, where the relative phase is accumulated quadratically with time, and
show that this can be produced by a variety of simple pulse sequences.
Interestingly, this scaling has a limited duration, and we show that certain
pulse sequences prolong the effect. The performance of these schemes is
analyzed and we examine their relevance to state-of-the-art experiments. We
analyze the $T^{3}$ scaling of the Fisher information which appears when
multiple synchronized measurements are performed, and is the optimal scaling in
the case of a finite coherence time.
