Suppose we have a uniform beam that is $4\mathrm{.}28$ metres long has a flexural rigidity of $29401N{m}^2.$

Find the deflection of the beam in millimetres if the beam is under a uniform load of $54\frac{N}{m}$ and is supported with fixed supports at both ends. Fill out the table below with your answers.

$x-$coordinate Deflection $(mm)$

$x=0\mathrm{.}60,y(x)=$

$x=1\mathrm{.}54,y(x)=$

$x=2\mathrm{.}40,y(x)=$

$x=3\mathrm{.}04,y(x)=$

$x=3\mathrm{.}55,y(x)=$

Enter as many decimal places as your calculator allows $(8$ to $10).$ Your answer must be within $+-0\mathrm{.}0005$ of the correct answer to be considered correct.