We study the expansion behaviors of a Fermionic superfluid in a cigar-shaped optical dipole trap for the whole BEC-BCS crossover and various temperatures. At low temperature (0.06(1)T), the atom cloud undergoes an anisotropic hydrodynamic expansion over 30 ms, which behaves like oscillation in the horizontal plane. By analyzing the expansion dynamics according to the superfluid hydrodynamic equation, the effective polytropic index γ¯ of Equation-of-State (EoS) of Fermionic superfluid is extracted. The γ¯ values show a non-monotonic behavior over the BEC-BCS crossover, and have a good agreement with the theoretical results in the unitarity and BEC side. The normalized quasi-frequencies of the oscillatory expansion are measured, which drop significantly from the BEC side to the BCS side and reach a minimum value of 1.73 around 1/ka=-0.25. Our work improves the understanding of the dynamic properties of strongly interacting Fermi gas.
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