# Homework Help: Solenoid electromechanical problem

1. Dec 1, 2011

### woody67

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.

Probel

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)