In this lesson, the focus is on understanding the time discretization and method of solving the matrix forms discussed. The matrix-vector problem of linear elastodynamics is written with the effect of structural damping (or Rayleigh damping) included. Time discrete matrix-vector equation is written and the Newmark family of algorithms is used to solve such equations. Newmark algorithm is explained for second-order ODEs. The a-method, correctors, and predictors are discussed. This is the standard solution approach for such problems.