  We experimentally investigate the periodic vortex shedding dynamics in a
highly oblate Bose-Einstein condensate using a moving penetrable Gaussian
obstacle. The shedding frequency $f_v$ is measured as a function of the
obstacle velocity $v$ and characterized by a linear relationship of
$f_v=a(v-v_c)$ with $v_c$ being the critical velocity. The proportionality
constant $a$ is linearly decreased with a decrease in the obstacle strength,
whereas $v_c$ approaches the speed of sound. When the obstacle size increases,
both $a$ and $v_c$ are decreased. The critical vortex shedding is further
investigated for an oscillating obstacle and found to be consistent with the
measured $f_v$. When the obstacle's maximum velocity exceeds $v_c$ but its
oscillation amplitude is not large enough to create a vortex dipole, we observe
that vortices are generated in the low-density boundary region of the trapped
condensate, which is attributed to the phonon emission from the oscillating
obstacle. Finally, we discuss a possible asymptotic association of $a$ with the
Strouhal number in the context of universal shedding dynamics of a superfluid.
