This paper is concerned with the small-amplitude oscillations of bubble composed of an ideal gas in response to an abrupt change in the ambient pressure field. Specifically, we consider the bubble response to a pressure pulse and a pressure step in an otherwise quiescent fluid. The method of analysis employed in the present study is a standard two-timing expansion to eliminate a secular behavior encountered in the asymptotic expansion. In the impulse response the secularity is self-induced due solely to the nonlinearity of the problem whereas the secularity in the step response arises from the change in the equilibrium bubble volume caused by the ambient pressure change. The two-timing solution for each response shows that the secularity modifies the natural frequency of the radial oscillation. Further, the critical intensity of either the pressure pulse or the pressure step for existence of the steady-state bubble radius is determined from the frequency modulated solution and the stability of the bubble response is also discussed in terms of the bubble compressibility and heat transfer across the interface.