  In this paper we have obtained the exact eigenstates of a two dimensional
damped harmonic oscillator in the presence of an external magnetic field
varying with respect to time in time dependent noncommutative space. It has
been observed that for some specific choices of the damping factor, the time
dependent frequency of the oscillator and the time dependent external magnetic
field, there exists interesting solutions of the time dependent noncommutative
parameters following from the solutions of the Ermakov-Pinney equation.
Further, these solutions enable us to get exact analytic forms for the phase
which relates the eigenstates of the Hamiltonian with the eigenstates of the
Lewis invariant. Then we compute the expectation value of the Hamiltonian. The
expectation values of the energy are found to vary with time for different
solutions of the Ermakov-Pinney equation corresponding to different choices of
the damping factor, the time dependent frequency of the oscillator and the time
dependent applied magnetic field. We also compare our results with those in the
absence of the magnetic field obtained earlier.
