The quantum oscillatory magnetization M(B) and chemical potential μ(B) of a two-dimensional (2D) electron system provide important and complementary information about its ground state energy at low temperature T. We developed a technique that provides both quantities in the same cool-down process via a decoupled static operation and resonant excitation of a micromechanical cantilever. On InGaAs/InP heterostructures, we observed beating patterns in both M(B) and μ(B) attributed to spin-orbit interaction. A significantly enhanced sensitivity in μ enabled us to extract Rashba and Dresselhaus parameters with high accuracy. The technique is powerful for detailed investigations on the electronic properties of 2D materials.