Aloudspeaker is a common electrochemical transducer in which vibration is caused by changes in the input current to a coil which, in turn, is coupled to a magnetic structure that can produce time- varying forces on the loudspeaker diaphragm. Figure (a) shows the schematic diagram of a loudspeaker, Figure (b) is a simplified model, Figure (c) is a free-body diagram of the forces acting on the loudspeaker diaphragm, and Figure (d) is the electrical model.

The force exerted on the coil is also exerted on the mass of the loudspeaker diaphragm.

Develop the equation of motion for the electrical and mechanical sides of the device and determine the frequency response U(jω)/V(jω) of the loudspeaker using phase analysis, and neglecting the coil inductance.