strong and zero or weak coupling between the nanomechanical oscillator and the electrons on the dot. The tunneling of electrons between the leads and the dot is considered to be symmetric (Γ$_{R}$ = Γ$_{L}$) and we assume that the leads have constant density of states. The dot population is shown in fig. 1, as a function of time in order to see the transient and steady state dynamics of the system. We consider here empty, half full and occupied states of the system for fixed values of Γ = 0 . 1 , η = 0 . 05 , by choosing the right and the left Fermi levels pairs ( 0, 0), (0, 1) and (1, 1) respectively. Firstly, when both the Fermi levels are below the dot energy then the dot population rises initially for a short time and for long times settles at a small but finite value. This is not quite empty because the finite Γ allows some tunneling onto the dot. Secondly, when the left Fermi level is above the dot energy then the dot population settles in a partially full (half full) state. Thirdly, when both the Fermi levels are above the dot energy, it is completely full for a short time but for long time is not quite full, again due to the dot coupling with the leads. These results are consistent with the particle-hole symmetry of the system as the empty state of the system is not empty and the occupied state is not completely full, while the partially full is roughly half full. In fig. 2, we have shown the total current flowing onto the dot as a function of time for fixed values of Γ = 0 . 1 , η = 0 . 05 , ϵ$_{F}$$_{R}$ = 0 , and of the left Fermi level 1. This current (solid line) is equivalent to the rate of change of the dot population (dashed line) for the same parameters. In this figure, we can not distinguish the solid and the dashed line. This confirms that our analytical results are consistent with the equation of continuity, I$_{L}$ ( t ) + I$_{R}$ ( t ) = d $_{dt}$ρ ( t ), and hence, with the conservation laws for all parameters. In fig. 3 we have shown the net current ( I$_{L}$ ( t ) − I$_{R}$ ( t )) flowing through the system as a function of both time and of the left Fermi level for two different values of coupling strength: η = 0 . 02 to η = 0 . 08 and for small and large values of Γ. We observe simple oscillations in the net current flowing through the system for weak coupling strength and weak tunneling. With increasing coupling strength the structure of the oscillations becomes more complicated as shown in fig. 3(b). In order to interpret this complicated structure, we have a two step discussion: firstly, we have plotted the net current as a function of time in fig. 4 with fixed values of the Fermi level, ϵ$_{F}$$_{L}$ = 1, ϵ$_{F}$$_{R}$ = 0 , tunneling energy, Γ = 0 . 01 and for different values of coupling strength: η = 0 . 02 and η = 0 . 08 . In this figure, in the limit of weak coupling the oscillations are again simple while for the strong coupling limit, there is a beating pattern in the oscillations. We note that the frequency of the simple oscillations 12