The electrodynamic shaker shown in Figure P13.49 is commonly used as a vibration tester. A...

The electrodynamic shaker shown in Figure P13.49 is commonly used as a vibration tester. A constant current is used to generate a magnetic field in which the armature coil of length l is immersed. The shaker platform with mass m is mounted in the fixed structure by way of a spring with stiffness k. The platform is rigidly attached to the armature coil, which slides on the fixed structure thanks to frictionless bearings.

a. Neglecting iron reluctance, determine the reluctance of the fixed structure, and hence compute the strength of the magnetic flux density B in which the armature coil is immersed.

b. Knowing B, determine the dynamic equations of motion of the shaker, assuming that the moving coil has resistance R and inductance L.

Figure P13.49 Electrodynamic shaker

c. Derive the transfer function and frequency response function of the shaker mass velocity in response to the input voltage VS.