A tunable mass-damping apparatus may include a housing having an interior surface, an interior volume containing a fluid, and an axis. The housing may be configured to be coupled to a wind tunnel model. The apparatus may further include a mass configured to move back and forth in the interior volume along the axis. The mass may be configured to make an airtight seal with the interior surface of the housing, thereby dividing the interior volume into an upper chamber and a lower chamber. The apparatus may include a passage fluidly connecting the upper chamber and the lower chamber and a spring configured to exert a position-dependent force upon the mass. The spring may be characterized by a variable spring constant chosen based on a variable natural frequency of a support structure of the wind tunnel model. The variable spring constant may be established with a nickel-titanium alloy spring heated to at least one calibrated temperature that corresponds to a predetermined spring constant.