$($e$)$ Use Euler's met JMERICAL

$x=L$

FIGURE P$1\mathrm{.}23$

A cantilever beam.

$2^{-15}s$ with $t=2^{-18}s$ given the initial co

$1\mathrm{.}23$ As depicted in Fig. P$1\mathrm{.}23,$ the downward deflection,

$y(m),$ of a cantilever beam with a uniform load, $w=10,000$

$k\frac{g}{m},$ can be computed as

$y=\frac{w}{24EI}(x^4-4L{x}^3+6L^2{x}^2)$

where $x=$ distance $(m),E=$ the modulus of elasticity $=$

$2{10}^{11}Pa,I=$ moment of inertia $=3\mathrm{.}25{10}^{-4}{m}^4,$ and $L=$

length $=4m.$ This equation can be differentiated to yield the

slope of the downward deflection as a function of $x$

$\frac{dy}{dx}=\frac{w}{24EI}(4x^3-12L{x}^2+12L^{2}x)$

If $y=0$ at $x=0,$ use this equation with Euler's method $(x=$

$0\mathrm{.}125$ m $)$ to compute the deflection from $x=0$ to $L.$ Develop

a plot of your results along with the analytical solution com$-$

puted with the first equation.

WITH MATLAB