# LINEARITY(waves and optics).

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We come across various physical problems where we have to compare a curved line with a straight line. These two curves may or may not be close to each other. Linearity is referred as closeness to which a curve approximates a straight line. The average curve is determined after making two or more full range transverses in each direction. The value of linearity is referred to the output. We know that if Steffen's S is constant , then the restoring force F is proportional to displacement × (f= -s×) and the oscillations are harmonic in nature. Also in such a case when the restoring force is plotted against displacement ×,it will give a straight line and the system is said to be linear. The displacement of a linear simple harmonic system follows a sine or cosine behavior. Non linearity result when stiffness constant S is not constant but varies with displacement ×. "The differential equation, which has terms depending only on the first power of the variable and it's derivative, is called linear differential equation". Also the equation is homogeneous if it has no terms independent of variable ×.

Linearity can be divided into three categories;

A) Independent linearity: this is the maximum deviation of actual characteristics (average of upscale and downscale readings) from a straight line so positioned as to minimize the maximum deviation fig. 1.6.1.

B) Terminal-based linearity: this is the maximum deviation of the actual characteristic(average of upscale and downscale readings)  from a straight line coinciding with the actual Characteristic at the upper and lower range value fig ;1.6.2

C) Zero-based reality : this is the maximum deviation of actual characteristic (average of upscale and downscale readings) from a straight line so positioned as to coincide with the actual characteristic at the lower range - value and to minimize the maximum deviation, fig :1.6.3