README.md

# Final_Project
#Problem 1
## 1.a
![Beam Deflection ](BeamDeflectionByLoading.png)
b. We used the Monte Carlo method for this part of the problem in order to determine the mean and standard deviatrion for the maximum deflection if b and h are normally dist. with q=50N/m.

#Problem 2
in order to solve for the system of equations for 6,10,20 segments, the following functions were used:

central_difference_6q.m

central_difference_10q.m

central_difference_20q.m

![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/Problem2graph.png)
#Problem 3
in order to solve for the system of equations for 6,10,20 segments, the following functions were used:

central_difference_6p.m

central_difference_10p.m

central_difference_20p.m

![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/Plot3a.png)
![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/plot3b.png)
![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/Plot3c.png)
#Problem 4

These the 6 segment beam yielded frequencies:
f1 = 141.7854
f2 = 529.1503
f3 = 1.0583e+03

These the 10 segment beam yielded frequencies:
f1 = 143.8803
f2 = 561.4373
f3 = 1.2118e+03

These the 20 segment beam yielded frequencies:
f1 = 144.7715
f2 = 575.5213
f3 = 1.2816e+03
![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/Prob4.png)