By the end of this section, you should be able to

1. Create FBDs for linear and rotational mechanical systems (single- and multi-element)

2. Use FBDs to derive EOMs for system

3. Use EOMs to create transfer functions for I/O forces/displacements for SMD systems

4. Use Mathematica to assist with algebraic steps in deriving TF

5. Use Matlab to simulate step- and impulse inputs into TF

This section focuses on transfer functions for mechanical systems and how they connect physical modeling to system response. You will start by building clear free body diagrams for linear and rotational elements, then use those diagrams to derive equations of motion with consistent sign conventions and input and output definitions. From the equations of motion, you will develop transfer functions that relate forces and displacements for spring mass damper systems, first for single degree of freedom models and then for multi degree of freedom systems. The emphasis is on a repeatable workflow that engineers actually use: define the input and output, write the governing differential equations, transform to the Laplace domain, solve for the transfer function, and check that the result makes physical sense.