We extend Tooru-Cohen analysis for nonequilirium steady state(NSS) of aBrownian particle to nonequilibrium oscillatory state (NOS) of Brownianparticle by considering time dependent externaldrive protocol. We consider an unbounded charged Brownian particle in thepresence of oscillatingelectric field and prove work fluctuation theorem, which is valid for anyinitial distribution and at alltimes. For harmonically bounded and constantly dragged Brownian particleconsidered by Tooru andCohen, work fluctuation theorem is valid for any initial condition(alsoNSS), but only in large timelimit. We use Onsager-Machlup Lagrangian with a constraint to obtainfrequency dependent workdistribution function, and describe entropy production rate and propertiesof dissipation functionsfor the present system using Onsager-Machlup functional.
