  A submerged body subject to a sudden shape-change experiences large forces
due to the variation of added-mass energy. While this phenomenon has been
studied for single actuation events, application to sustained propulsion
requires studying \textit{periodic} shape-change. We do so in this work by
investigating a spring-mass oscillator submerged in quiescent fluid subject to
periodic changes in its volume. We develop an analytical model to investigate
the relationship between added-mass variation and viscous damping and
demonstrate its range of application with fully coupled fluid-solid
Navier-Stokes simulations at large Stokes number. Our results demonstrate that
the recovery of added-mass kinetic energy can be used to completely cancel the
viscous damping of the fluid, driving the onset of sustained oscillations with
amplitudes as large as four times the average body radius $r_0$. A quasi-linear
relationship is found to link the terminal amplitude of the oscillations $X$,
to the extent of size change $a$, with $X/a$ peaking at values from 4 to 4.75
depending on the details of the shape-change kinematics. In addition, it is
found that pumping in the frequency range of
$1-\frac{a}{2r_0}<\omega^2/\omega_n^2<1+\frac{a}{2r_0}$ is required for
sustained oscillations. The results of this analysis shed light on the role of
added-mass recovery in the context of shape-changing bodies and
biologically-inspired underwater vehicles.
