  We study experimentally the thermal fluctuations of energy input and
dissipation in a harmonic oscillator driven out of equilibrium, and search for
Fluctuation Relations. We study transient evolution from the equilibrium state,
together with non equilibrium steady states. Fluctuations Relations are
obtained experimentally for both the work and the heat, for the stationary and
transient evolutions. A Stationary State Fluctuation Theorem is verified for
the two time prescriptions of the torque. But a Transient Fluctuation Theorem
is satisfied for the work given to the system but not for the heat dissipated
by the system in the case of linear forcing. Experimental observations on the
statistical and dynamical properties of the fluctuation of the angle, we derive
analytical expressions for the probability density function of the work and the
heat. We obtain for the first time an analytic expression of the probability
density function of the heat. Agreement between experiments and our modeling is
excellent.
