When liquid in a U-tube of uniform cross-section is displaced by $x$, the restoring force comes from the pressure difference of a $2x$ height column: $F = -\rho A g(2x)$. This gives SHM with $\omega^2 = 2g/l$ where $l$ is the total length of liquid column. Time period: $T = 2\pi\sqrt{l/(2g)}$. Note the factor of 2: the effective restoring force involves $2x$ because when one side goes up by $x$, the other goes down by $x$.