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Homework Help: Solenoid electromechanical problem

  1. Dec 1, 2011 #1
    1. The problem statement, all variables and given/known data
    We have a solenoid and power supply and a plunger with a mass,
    Determine y(t) when v(t)=U(t) (i.e the movement of the plunger when the input voltage is the unit step) use laplace transformes for the current i(s) and for the movement of the mass for a given force.


    2. Relevant equations

    voltage generated by movement of plunger = Vb(t) = N x dy/dt
    voltage across the winding = V(t)
    Current across the winding = i(t)

    The magnetic field induces a force the magnitude of this force is related to the current in the windings via the solenoids electro magnetic coupling constant N shown as

    f(t) =N i(t)

    3. The attempt at a solution

    Current in the system can be seen using Kirchoffs voltage law:

    v(t) = ia x Ra + L dia/dt + N dy/dt
    Laplace transform for the above:
    V(s) = Ia(s)Ra+LasIa(s)+Nsx(s)
    collected Ia(s)

    V(s) = Ia(s)(Ra+Las)+Nsx(s)

    I am struggling to glue the mechanical and electrical together and am unsure as to what i need to do with the f(t)=Ni(t)
  2. jcsd
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