The whipping instability in electrospinning of a viscoselastic jet is considered. The whipping motion of the jet during electrospinning is generally conjectured to initiate the large drawdown required to generate polymeric nanofibers. The phenomenon plays a dominant role in determining the characteristic strain rate at which a fluid filament is deformed during the drawdown. The stability of the whipping process also plays a critical role in determining the quality of the fibers obtained. The whipping motion is studied by passing a laser beam through the whipping region such that the beam is intercepted by the jet at intervals of time. The beam interception events are manifested as regular drops in the detector voltage. Subsequent analysis of the detector signals provides information on the periodicity of the jet's motion. It is demonstrated that with increasing accelerating voltage temporal order-disorder and disorder-order transitions occur in the motion of the electrified jet. The possibility of these transitions resulting from the pulsation of the Taylor cone from which the jet emanates is also considered. Additionally, similarities of the process with the nonlinear dynamics of neutral and electrified dripping faucets are also discussed.