Oscillations with periods on the order of 5–10 min have been observed by instrumented spacecrafts in the Earth's magnetosphere. These oscillations often follow sudden impacts related to coronal mass ejections. It is demonstrated that a simple model is capable of explaining these oscillations and give a scaling law for their basic characteristics in terms of the basic parameters of the problem. The period of the oscillations and their anharmonic nature, in particular, are accounted for. The model has no free adjustable numerical parameters. The results agree well with observations. The analysis is supported by numerical simulations solving the Magneto-Hydro-Dynamic (MHD) equations in two spatial dimensions, where we let a solar wind interact with a magnetic dipole representing a magnetized Earth. We consider two tilt-angles of the magnetic dipole axis. We find the formation of a magnetosheath with the magnetopause at a distance corresponding well to the analytical results. Sudden pulses in the model solar wind sets the model magnetosphere into damped oscillatory motions and quantitatively good agreement with the analytical results is achieved.