added lab 4 to main repo

README.md

@@ -22,8 +22,26 @@ The group shares the pass/fail grade for the "lab report" grade.
 then follow the link to the class server.*
 
 # [ugmelab.uconn.edu](https://ugmelab.uconn.edu) 
+# ME3263 Introduction to Sensors and Data Analysis (Fall 2018)
 
-# ME 3263 Introduction to Sensors and Data Analysis (Fall 2018)
+## Lab #4 Predicting Natural Frequencies with the Finite Element Method
+
+
+### What is the Finite Element Method?
+
+The Euler-Lagrange dynamic beam equation is an example of a partial differential
+equation (PDE). These equations are common in many engineering applications e.g.
+solid mechanics, electromagnetics, fluid mechanics, and quantum mechanics. The
+finite element method solves PDEs. The FEM process involves two steps to create
+matrices for a computer algorithm solution. First, the PDE is integrated from
+the strong form to the weak form. Second, an approximation of the variable
+"shapes" within each "element" is created to convert the integrals and
+derivatives into matrices
+[(1)](http://bcs.wiley.com/he-bcs/Books?action=index&bcsId=3625&itemId=0470035803).
+For elements with nodes only at vertices, such as cubes (hexahedrons) or
+pyramids (tetrahedrals), the "shape" function is linear for displacement. 
+
+[Lab 4 github files](https://github.uconn.edu/rcc02007/ME3263-Lab_04.git)
 
 ## Lab #3 Measuring Natural Frequencies