I. Find the equation of motion using any of the following methods;

a$.$ Using Newton's Method,

b$.$ Using the D'Alembert method

c$.$ Using the Energy Method

d$.$ Using Lagrange's Method,

II$.$ Find the natural frequencies using any methods,

III. Find the mode shapes and nodes corresponding to the natural frequencies found

IV$.$ Graph the mode shapes and nodes and interpret the graphs.

For all systems, SCD will be drawn, derivations will be made, solutions will be shown and the assignment will be sent in numerical format to $.$Imsclus, until due date $($its stated in Imsclus$).$ The initial displacement and velocity will be chosen by the student and the chosen value will be indicated. MS Word application will be used in writing, all equations will be written in MathType or MS Equation Editor$).$