Question $4(25$ Marks $)$

a$)$ An engineering student desires to make an instrument for measuring force. She decides to use a spring to achieve this. With illustration$($s$)$ derive the mathematical model governing this phenomena that force causes displacement.

b$)$ Table Q$4$ tabulates the data obtained from the instrument functional tests. Plot the data and determine the equalizing constant.

Table Q$4$

$\backslash$table$[[$S$/$No$.,\backslash$table$[[$Displacement$],[(mm)$