  Floquet analysis of modulated magnetoconvection in Rayleigh-B\'{e}nard\
geometry is performed. The temperature of the lower plate is varied
sinusoidally in time about a finite mean. As the Rayleigh number $\mathrm{Ra}$
is made to cross a critical value $\mathrm{Ra}_o$, the oscillatory
magnetoconvection begins. The flow at the onset of magnetoconvection may
oscillate either subharmonically or harmonically with the external modulation.
The critical Rayleigh number $\mathrm{Ra}_o$ varies non-monotonically with
$\omega$ for appreciable value of $a$. The temperature modulation may either
postpone or prepone the appearance of magnetoconvection. The magnetoconvective
flow always oscillates harmonically at larger values of $\omega$. The threshold
$\mathrm{Ra}_o$ and the corresponding wave number $k_o$ approach to their
values for the stationary magnetoconvection in the absence of modulation ($a =
0$), as $\omega \rightarrow \infty$. Two different zones of harmonic
instability merge to form a single instability zone with two local minima for
higher values of Chandrasekhar's number $\mathrm{Q}$, which is qualitatively
new. We have also observed a new type of bicritical point, which involves two
different sets of harmonic oscillations. The effects of variation of
$\mathrm{Q}$ and $\mathrm{Pr}$ on the threshold $\mathrm{Ra}_o$ and critical
wave number $k_o$ are also investigated.

Fluid Dynamics