This is a proposal to measure the magnetic spectrum of single crystal La2-xBaxCoO4 for the first time. The isostructural layered cobaltates with Sr and Ca instead of Ba have been studied extensively. The x=1/2 composition exhibits long-range checkerboard charge order and accompanying antiferromagnetic order, but the x = 1/3 composition is more complex. It has a nanoscale coexistence of different electronic phases, including period-3 spin-charge stripes, and has a distinctive hourglass-shaped magnetic spectrum. The Ba-doped system has not been investigated previously. Our objective is to obtain a complete mapping in energy and momentum of the magnetic spectrum of La2-xBaxCoO4 with x = 1/3 and 1/2. The results will be compared with the known spectra of La2-xSrxCoO4, and by analysing the spectra quantitatively we hope to gain a picture of the electronic ground state in these systems.