- #1
erahartman
- 7
- 0
Here is a doozy
In a magnetic levatation experiment a metallic object is help up in the air suspended under an electromagnet. The vertical displacement of the object can be described by the following nonlinear differential equation.
m(d^2H/dt^2)=mg-k(I^2/H^2)
m=mass of object
g=gravity acc const
k=const
H=distance between electromagnet and object (output signal)
I=electromagnet current ( input signal)
a) show that the system is in equilibrium when
Ho=Io*sqrt(k/mg)
b) Linearize the equation about the equilibrium point found in part a and show that the resulting transfer function obtained from the linearized differential equation can be expressed as
(deltaH(S)/deltaI(s))=-a/(s^2-b^2)
a>0
In a magnetic levatation experiment a metallic object is help up in the air suspended under an electromagnet. The vertical displacement of the object can be described by the following nonlinear differential equation.
m(d^2H/dt^2)=mg-k(I^2/H^2)
m=mass of object
g=gravity acc const
k=const
H=distance between electromagnet and object (output signal)
I=electromagnet current ( input signal)
a) show that the system is in equilibrium when
Ho=Io*sqrt(k/mg)
b) Linearize the equation about the equilibrium point found in part a and show that the resulting transfer function obtained from the linearized differential equation can be expressed as
(deltaH(S)/deltaI(s))=-a/(s^2-b^2)
a>0