Problem $1[50$ pts$]$

Resolve Lecture $6\text{'}$s Bernoulli beam example problem with Pinned Boundary Conditions on the

left end $($at $x=0)$ and fixed Boundary Conditions on the right end $($at $x=0).$ Pinned Boundary

Conditions are described by $w(x)=w^{\text{'}\text{'}}(x)=0.$ Use just enough nodes for the solution to

converge with a $0\mathrm{.}5\%$ relative improvement from the previous iteration.

Deliverables$($Submit the code electronically as LastName$\_$Problem$1.$m anda PDF file

publication$)$

By hand, write the definitions of the Boundary conditions in FDM $($submit any

handwritten portion in PDF as well$).$

Write the first two equations into the solution stiffness matrix, including one of the B$.$C$.$

itself $($first equation$)$ and the ODE $($second equation$)$ after the second B$.$C modifies it$.$

Solve the problem in Matlab using the constant load condition from the Lecture.

Compare the solution to the solution from Lecture $6\text{'}$s example.