The response of the magnetopause surface to time-varying solar wind dynamic pressure is examined. We argue that to a first approximation the magnetopause surface may be considered as analogous to an elastic membrane. Upon displacement from equilibrium resulting from a change in applied external pressure, it moves to a new equilibrium under the equation of motion of a forced, damped, simple harmonic oscillator. We derive this equation of motion by linearising for small perturbations the momentum equation for flow past a nonrigid ellipsoidal body in the Newton-Busemann limit. Though our approach is only an approximation to the real dynamics of the magnetopause boundary, it serves to demonstrate the importance of inertia in the system response. It allows us to estimate the natural eigenperiod of magnetopause oscillation as typically around 7 min, the precise value depending on solar wind conditions. However, the magnetopause eigenoscillation is furthermore found to be strongly damped, regardless of solar wind conditions. One consequence of these properties is that short-period fluctuations in the solar wind dynamic pressure elicit a suppressed magnetospheric response. We outline other theoretical expectations by which our model may be tested against observation, and discuss the implications of our findings for current interpretations of spacecraft observations made in the dynamic magnetopause environment.