Vortex-induced vibration of a circular cylinder with low mass ratio (
$0.05\leqslant m^{\ast }\leqslant 10.0$
) is investigated, via a stabilized space–time finite element formulation, in the laminar flow regime where
$m^{\ast }$
is defined as the ratio of the mass of the oscillating structure to the mass of the fluid displaced by it. Computations are carried out over a wide range of reduced speed,
$U^{\ast }$
, which is defined as
$U/f_{N}D$
, where
$U$
is the free-stream speed,
$f_{N}$
the natural frequency of the spring mass system in vacuum and
$D$
the diameter of the cylinder. In particular, the situation where the lock-in regime extends up to infinite reduced speed is explored. Studies at large
$Re$
, in the past, have shown that the normalized amplitude of cylinder oscillation at infinite reduced speed,
$A_{\infty }^{\ast }$
, exhibits a sharp increase when
$m^{\ast }$
is reduced below the critical mass ratio (
$m_{crit}^{\ast }$
). This jump signifies a shift from desynchronized response to lock-in state. In this work it is shown that in the laminar regime, a jump in
$A_{\infty }^{\ast }$
occurs only beyond a certain
$Re$
(
$=Re_{j}\sim 108$
). For
$Re<Re_{j}$
, the response increases smoothly with decrease in
$m^{\ast }$
with no discernible jump. In this situation, therefore, the identification of
$m_{crit}^{\ast }$
based on jump in response at
$U^{\ast }=\infty$
is not possible. The difference in the
$A^{\ast }-m^{\ast }$
variation on the two sides of
$Re=Re_{j}$
, is attributed to the difference in the transition between the lower branch of cylinder response and desynchronization regime. This transition is brought out more clearly by plotting
$A^{\ast }$
with
$f_{v_{o}}/f$
, where
$f_{v_{o}}$
is the vortex shedding frequency for the flow past a stationary cylinder and
$f$
is the cylinder vibration frequency. In the
$A^{\ast }-f_{v_{o}}/f$
plane, the response data as well as other quantities related to free vibrations, for different
$m^{\ast }$
, collapse on a curve. Unlike at high
$Re$
, the collapsed curves show a dependence on
$Re$
in the laminar regime. The transition between the lock-in and desynchronized state, as seen from the collapsed curves, is qualitatively different for
$Re$
on either side of
$Re_{j}$
. The collapsed curves, at a certain
$Re$
, are utilized to estimate
$A^{\ast }$
for the limiting case of
$(U^{\ast },m^{\ast })=(\infty ,0)$
. Interestingly, unlike at large
$Re$
, this limit value is found to be lower than the peak amplitude of cylinder vibration at a given
$Re$
. Hysteresis in the cylinder response, near the higher-
$U^{\ast }$
end of the lock-in regime, is explored. It is observed that the range of
$U^{\ast }$
with hysteretic response increases with decrease in
$m^{\ast }$
. Interestingly, for a certain range of
$m^{\ast }$
, the response is hysteretic from a finite
$U^{\ast }$
up to
$U^{\ast }=\infty$
. We refer to this phenomenon as hysteresis forever. It occurs because of the existence of multiple response states of the system at
$U^{\ast }=\infty$
, for a certain range of
$m^{\ast }$
. The study brings out the significant differences in the response of the fluid–structure system associated with the critical mass phenomenon between the low- and high-
$Re$
regime.