In the Coriolis sensor, the tubes correspond to the spring. The mass of the tubes plus the mass of the fluid they contain, correspond to the mass at the end of the spring. The stiffness of the flow tubes remain essentially constant. Therefore, the mass (density) of the fluid contained in the fixed volume of the flow tubes is the only variable effecting the natural frequency.
During operation, a drive coil causes the tubes to oscillate at their natural frequency.
As the mass of the process fluid increases, the natural frequency decreases (increase the mass)
As the mass of the process fluid decreases, the natural frequency increases (decrease the mass)