We investigate the effect of frequency mismatch in two indirectly coupled Rossler oscillators and Hindmarsh-Rose neuron model systems. While identical systems show in-phase or out-of-phase synchronization states when coupled through a dynamic environment, mismatch in the internal frequencies of the systems drives them to a fixed point state, i.e., amplitude death. There is a region in the parameter space of the frequency mismatch and coupling strength where system shows amplitude death. The numerical results of Rossler system are also experimentally verified using piece-wise Rossler circuits. (C) 2012 Elsevier B.V. All rights reserved.