  We analyze a version of the sine-Gordon model in which the strength of the
cosine potential has a periodic dependence on time. This model can be
considered as the continuum limit of the many body generalization of the
Kapitza pendulum. Based on the perturbed CFT point of view, we develop a
truncated conformal space approach (TCSA) to investigate the Floquet
quasienergy spectrum. We focus on the effective behaviour for large driving
frequencies, which we also derive exactly. Depending on the driving protocol,
we can recover the original sine-Gordon model or its two-frequency version. The
rich structure of the two-frequency model implies that the time-periodic drive
can break integrability, can lead to new states in the spectrum or can result
in a phase transition. Our method is applicable for any periodically driven
perturbed conformal field theories.
