The plunger with mass M shown in Fig. 2.10-5 is free to move within an electroma

Question

The plunger with mass M shown in Fig. 2.10-5 is free to move within an electromagnet. Although the winding of the electromagnet consists of many turns, only one is shown. The mechanical damping varies directly as the surface area of the plunger within the electromagnet, (a) Write the voltage equation for the electric system. (b) Write the dynamic equation for the mechanical system. Include the force of gravity, (c) Express the mechanical damping D. (d) Express the electromagnetic Figure 2.10-5: Cross section of plunger system. force fe if i = a lambda2 + b lambda (x - d)2. (e) Express the steady-state position x for a constant current flowing in the winding.

Explanation / Answer

plunger system is an electrical equilent of solenoid (strandard magnetic) circuit

the inductance of the solenoid can be expressed as

L(x)=

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