  Using Monte Carlo simulations, we study the hysteresis in unzipping of a
double stranded DNA whose ends are subjected to a time dependent periodic force
with frequency ($\omega$) and amplitude ($G$). For the static force, i.e.,
$\omega \to 0$, the DNA is in equilibrium with no hysteresis. On increasing
$\omega$, the area of the hysteresis loop initially increases and becomes
maximum at frequency $\omega^{*}(G)$, which depends on the force amplitude $G$.
If the frequency is further increased, we find that for lower amplitudes the
loop area decreases monotonically to zero, but for higher amplitudes it has an
oscillatory component. The height of subsequent peaks decrease and finally the
loop area becomes zero at very high frequencies. The number of peaks depends on
the length of the DNA. We give a simple analysis to estimate the frequencies at
which maxima and minima occurs in the loop area. We find that the area of the
hysteresis loop scales as $1/\omega$ in high-frequency regime whereas, it
scales as $G^{\alpha} \omega^{\beta}$ with exponents $\alpha =1$ and $\beta =
5/4$ at low-frequencies. The values of the exponents $\alpha$ and $\beta$ are
different from the exponents reported earlier based on the hysteresis of small
hairpins.
