Wavepacket dynamics in the ground electronic state of a diatomic molecule is considered using a model which involves two electronic states coupled by two infinitely short light pulses. Electronic states are modeled by shifted harmonic oscillators with different frequencies. Exact expressions for wavepackets in ground and excited states are obtained. The spatial and spectral characteristics of the wavepackets are studied as functions of molecular parameters and delay time between pump and dump pulses. It is shown that spatial and spectral widths of wavepackets in the ground state can be controlled by varying the delay time. The possibility of creating squeezed wavepackets is discussed.