Fall 2001 16.311-8 System Modeling Investigate the model of a simple system to explore the basics of system dynamics Provide insight on the connection between the system response d the pole locations M2 Consider the simple mechanical system(2MSS)-derive the system model 1. Start with a free body diagram 2. Develop the 2 equations of motion m1=k(x2-x1) k( )+F 3. How determine the relationships between 1, c2 and F? Numerical integration- good for simulation, but not analysis Use laplace transform to get transfer functions Fast /easy/lots of tables k Provides lots of information(poles and zeros)Fall 2001 16.31 1—8 System Modeling • Investigate the model of a simple system to explore the basics of system dynamics. — Provide insight on the connection between the system response and the pole locations. • Consider the simple mechanical system (2MSS) — derive the system model 1. Start with a free body diagram 2. Develop the 2 equations of motion m1x¨1 = k(x2 − x1) m2x¨2 = k(x1 − x2) + F 3. How determine the relationships between x1, x2 and F? — Numerical integration - good for simulation, but not analysis — Use Laplace transform to get transfer functions ∗ Fast/easy/lots of tables ∗ Provides lots of information (poles and zeros)