A tachometer $($a$.$k$.$a$.$ tach$)$ is an electromechanical sensor that produces an output voltage that is proportional to a mechanical shaft angular velocity input. The intermediate mechanism

between the two is a gear connected to an armature controlled motor. A tach is essentially a motor$/$gear system operating in reverse. This tells the customer how fast a shaft is spinning.

Create the system dynamics transfer function from input shaft angular velocity, ${}_w,$ to output voltage $V_m$ using the standard method of creating free body diagrams, electrical diagrams,

solving Newton's law, solving Kirchoff's law, Laplace transform, apply gear constraints, and solve the result for the desired transfer function.