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The work fluctuations of an oscillator in contact with a heat reservoir anddriven out of equilibrium by an external force are studied experimentally. Theoscillator dynamics is modeled by a Langevin equation. We find bothexperimentally and theoretically that, if the driving force does not change theequilibrium properties of the thermal fluctuations of this mechanical system,the free energy difference $\Delta F$ between two equilibrium states can beexactly computed using the Jarzynski equality (JE) and the Crooks relation (CR)\cite{jarzynski1, crooks1, jarzynski2}, independently of the time scale andamplitude of the driving force. The applicability limits for the JE and CR atvery large driving forces are discussed. Finally, when the work fluctuationsare Gaussian, we propose an alternative empirical method to compute $\Delta F$which can be safely applied, even in cases where the JE and CR might not hold.The results of this paper are useful to compute $\Delta F$ in complex systemssuch as the biological ones.Comment: submitted to Journal of Statistical Mechanics: Theory and experimen

Estimate of the free energy difference in mechanical systems from work fluctuations: experiments and models