  We propose a practically feasible time-periodic sinusoidal drive protocol in
onsite mass term to generate the two-dimensional~(2D) Floquet second-order
topological superconductor, hosting both the regular $0$- and anomalous
$\pi$-Majorana corner modes~(MCMs) while starting from a static 2D topological
insulator/$d$-wave superconductor heterostructure setup. We theoretically study
the local density spectra and the time dynamics of MCMs in the presence of such
drive. The dynamical MCMs are topologically characterized by employing the
average quadrupolar motion. Furthermore, we employ the Floquet perturbation
theory~(FPT) in the strong driving amplitude limit to provide analytical
insight into the problem. We compare our exact (numerical), and the FPT results
in terms of the eigenvalue spectra and the time dynamics of the MCMs. We
emphasize that the agreement between the exact numerical and the FPT results
are more prominent in the higher frequency regime for close to the
$0$-quasi-energy mode.
