A magnetic transducer shown consists of a wedge
-
shaped piece of metal
(
moment of inertia


about pin at


)
that is free to rotate though the angle

,
where

is the angular deflection of the wedge center line from the center line of the device. A magnetic field is produced by means of an electric circuit that has a voltage source, resistance, and inductance. This magnetic field induces a torque

exerted on the wedge
(
proportional to the circuit current
)
,
while a torsional spring opposes the rotation of the wedge. The motion of the wedge in turn produces a back emf
(
proportional to the angular velocity
)
in the electric circuit. a
.
Decouple the system into its electrical and mechanical subsystems and draw the decoupled subsystems. b
.
Determine the mathematical models of the system being sure to start with appropriate schematics and fundamental laws. c
.
Transfer Function Practice: Find the system transfer functions for current and angular deflection. d
.
Block Diagramming Practice: Construct a block diagram which has the voltage source

(

)
as the input and output lines for angular acceleration, angular velocity, and angular position of the movable wedge mass and current generated in the electric circuit.