  We have performed a systematic study of the log$ft$ values, shape factors and
electron spectra for the second-forbidden nonunique $\beta^-$ decays of
$^{24}$Na$(4^+) \rightarrow ^{24}$Mg$(2^+)$ and $^{36}$Cl$(2^+) \rightarrow
^{36}$Ar$(0^+)$ transitions under the framework of the nuclear shell model. We
have performed the shell model calculations in the $sd$ model space, using more
recent microscopic effective interactions such as Daejeon16, chiral N3LO, and
JISP16. These interactions are derived from the no-core shell model wave
functions using Okubo-Lee-Suzuki transformation.For comparison, we have also
shown the results obtain from the phenomenological USDB interaction. To test
the predictive power of these interactions first we have computed low-lying
energy spectra of parent and daughter nuclei involved in these transitions. The
computed results for energy spectra, nuclear matrix elements, log$ft$ values,
shape factors, electron spectra and decomposition of the integrated shape
factor are reported and compare with the available experimental data.
