What is order instrument?

Answer 1

A second order linear instrument has an output which is given by a non-homogeneous second order linear differential equationd2y(t)/dt2 + 2.rho.omega.dy(t)/dt + omega2.y(t) = K.omega2.x(t),

where rho is a constant, called the damping factorof the instrument, and omega is a constant called the natural frequency of the instrument.

Under a static input a second order linear instrument tends to oscillate about its position of equilibrium. The natural frequency of the instrument is the frequency of these oscillations.

Friction in the instrument opposes these oscillations with a strength proportional to the rate of change of the output. The damping factor is a measure of this opposition to the oscillations.

An example of a second order linear instrument is a galvanometer which measures an electrical current by the torque on a coil carrying the current in a magnetic field. The rotation of the coil is opposed by a spring. The strength of the spring and the moment of inertia of the coil determine the natural frequency of the instrument. The damping of the oscillations is by mechanical friction and electrical eddy currents.

Another example of a second order linear instrument is a U-tube manometer for measuring pressure differences. The liquid in the U-tube tends to oscillate from side to side in the tube with a frequency determined by the weight of the liquid. The damping factor is determined by viscosity in the liquid and friction between the liquid and the sides of the tube.