$2$

Table $1$ is for the specific parameters assigned to the group for this assignment. These parameters will be used in the calculations and analyses required.

Table $1$ Reference to Parameters

$\backslash$table$[[$The last digit of the matric number$*,0,2,1,3,4,6,5,7,8,9],[$A $($m$),3\mathrm{.}0,3\mathrm{.}2,2\mathrm{.}8,3\mathrm{.}4,3\mathrm{.}8],[$B $($m$),0\mathrm{.}5$ A$,0\mathrm{.}5A,0\mathrm{.}5A,0\mathrm{.}5A,0\mathrm{.}5$ A$],[\backslash$table$[[*$Example for choosing parameters:$],[$Matric number student $1={50078}_{?},$ and matric number student $2={50071}_{?}.$ The last digit of the matric number $=8_{+}{7}_{?}={15}_{\text{;}}{1}_{+}{5}_{?}=6_{?}.$ Therefore, $A=2\mathrm{.}8m,B=0\mathrm{.}5Am,$ etc.$]]]]$

Question $1(30$ marks$)$

You are tasked with analyzing an asymmetrical trapezoidal steel plate, as shown in

Figure $1.$ The plate has a uniform thickness of $0\mathrm{.}3$ m but a nonuniform, linearly varying density along the $x-$axis, where the density at the left edge