  In whispering gallery mode resonator sensing applications, the conventional
way to detect a change in the parameter to be measured is by observing the
steady state transmission spectrum through the coupling waveguide.
Alternatively, cavity ring-up spectroscopy (CRUS) sensing can be achieved
transiently. In this work, we investigate CRUS using coupled mode equations and
find analytical solutions with a large spectral broadening approximation of the
input pulse. The relationships between the frequency detuning, coupling gap and
ring-up peak height are determined and experimentally verified using an
ultrahigh \textit{Q}-factor silica microsphere. This work shows that
distinctive dispersive and dissipative transient sensing can be realised by
simply measuring the peak height of the CRUS signal, which might improve the
data collection rate.
