MATLAB exercise Consider sectioning your code. Debug your

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Question $1$: Suppose we have a supported beam with a uniformly distributed load. The deflection $($y$)$ of the beam at any point x along its length can be approximated by the following equation:

y$($x$)=$ W$0/120$EIL$(-5$x$^2=2$L$^2$x$^3-$L$^4$x$)$

Where W$0$ is the uniformly distributed load $($force per unit length$),$ E is Young$$s modulus of

the material, I is the moment of inertia of the beam$$s cross$-$sectional area, L is the length of the

beam, and x is the distance along the beam.

PART A:

Write a MATLAB function to calculate the deflection for value$($s$)$ of x$.$ Input in the code W$0=2\mathrm{.}5$ KN$/$cm$,$ E$=50,000$ KN$/$cm$^2,$ I$=30,000$ cm$^4,$ and L$=600$ cm$.$ Enable the code to:

$$ calculate the deflection

$$ determine the maximum deflection and maximum deflection locations using MATLAB$$s

built$-$in function $$min$.$ The $$min$$ function in MATLAB returns the minimum value and

the index where that minimum value occurs in the input vector $($for more information help

min command$).$

syntax: $[$min$\_$value, index$]=$min$($variable name of the array containing all values$)$

Note that deflection values are negative numbers, and the max deflection $=$min value.

$$ use the index $($from the above output$)$ to identify the location of maximum deflection of

vector x$.$

Example vector x contains $5$ data points, then write a code to find the data that is stored in

row $2($in this case index$=2)$

$-$ x$=[2,3,5,7,9]$; then x$(2)=3$

$$ plot the deflection y$($x$)$ along the length of the beam

$$ mark the point of maximum deflection on the plot

PART B:

Call the function you build in a$,$ and evaluate the function for x values ranging from $0$ to L

with a step size $10.$

Publish the code in a$,$ the function call in b and the corresponding outputs. The code should

provide an array of deflection, an array of maximum deflection, an array of locations of

maximum deflection, a plot of y vs x and a mark showing the point of maximum deflection on

the plot.

Hint:

$$ Use MATLAB$$s plot function to mark the point of max deflection $($use maximum

deflection value and location as inputs$)$

$$ Consider adding deflection, maximum deflection and location of maximum deflection

as the function output variables.