Eigenvalue assignment problem is a classical problem in system control theory. Based on the receptance matrix method, this paper studies the partial eigenvalue assignment of second-order control systems, and analyzes the sensitivity of closed-loop systems. In partial eigenvalue assignment, a non overflow algorithm for partial eigenvalue assignment is established by using the orthogonal relationship between system matrix and eigenvalue matrix. The algorithm does not need to solve Sylvester equation, and the configuration of target eigenvalues can be realized through a small part of information. In addition, we also establish the response matrix method for the sensitivity allocation of eigenvalues and eigenvectors. Finally, an example shows the effectiveness of the algorithm.