README.md

# final_proj_group11

# Problem 1
Used functions/scripts:

a. shape_simple_support.m, PlotSSS.m

b. montecarlo.m

![q versus maximum deflection](Plot1.PNG)

# Problem 2
Used functions/scripts:

a-d: CDM.m, plotCDM_Part_2.m

![q versus maximum deflection for various N](Plot2.PNG)

e: The script plotCDM_Part_2.m calls the function CDM.m (documented in help file) to generate 
deflection values for the given set of values of q, plots them against the q values

# Problem 3
Used functions/scripts:

a-d: CDM.m, plotCDM_Part_3.m

![q versus maximum deflection for various N and P](Plot3.PNG)

# Problem 4
Used functions/scripts:

a-d: egv.m, defl.m, solveODE.m

6 Segments -- called with egv(6,0) -- all in hz

| First Natural Frequency | Second Natural Frequency | Third Natural Frequency |
| ------------- | ------------- | ------------- |
| 141.7854  | 529.1503  | 1.0583e+03  |

10 Segments -- called with egv(10,0) -- all in hz

| First Natural Frequency | Second Natural Frequency | Third Natural Frequency |
| ------------- | ------------- | ------------- |
| 143.8803  | 561.4373  | 1.2118e+03  |

20 Segments -- called with egv(20,0) -- all in hz

| First Natural Frequency | Second Natural Frequency | Third Natural Frequency |
| ------------- | ------------- | ------------- |
| 144.7715  | 575.5213  | 1.2816e+03  |

e.

![NEW BEAM POSITION!!](Plot4.png)

note: We couldn't analytically solve for the initial conditions for the first and third derivatives (or they were not given), so this is what we got.