  We propose a generic model of driven DNA under the influence of an
oscillatory force of amplitude $F$ and frequency $\nu$ and show the existence
of a dynamical transition for a chain of finite length. We find that the area
of the hysteresis loop, $A_{\rm loop}$, scales with the same exponents as
observed in a recent study based on a much more detailed model. However,
towards the true thermodynamic limit, the high-frequency scaling regime extends
to lower frequencies for larger chain length $L$ and the system has only one
scaling ($A_{\rm loop} \approx \nu^{-1}F^2)$. Expansion of an analytical
expression for $A_{\rm loop}$ obtained for the model system in the low-force
regime revealed that there is a new scaling exponent associated with force
($A_{\rm loop} \approx \nu^{-1}F^{2.5}$), which has been validated by
high-precision numerical calculation. By a combination of analytical and
numerical arguments, we also deduce that for large but finite $L$, the
exponents are robust and independent of temperature and friction coefficient.
