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$x$.