A uniform spring of force constant $120\ \text{N/m}$ is cut into two pieces whose lengths are in the ratio $1 : 2$. A block of mass $0.60\ \text{kg}$ lies on a smooth table between two walls, with the short piece joining it to one wall and the long piece to the other. Both pieces have their natural lengths when the block is at rest. What is the angular frequency of small oscillations of the block? Give the answer in $\text{rad/s}$.