Natural Fraquency and Model Shape Classical Approach The modal shapes, frequencies and the modal damping vataneрр characteristics of a structure. The free undamped vibration equation of motion is the basic one for solving these parameters and is given by (1) [M]{*}+[k] {x}=0 …(1) The natural frequencies are exactly determinable from the frequency determinant: [k]-p[M]=0 …(2) The modal patterns can be obtained from the equation ((k]-p* [M)(x}=0 …(3) where {x} is the vector of amplitudes. A second method is to convert the equation (1) into the mathematical eigen value problem. Defining D] as the dynamic matrix=[M](], the oquation (1) reduces to the form {D} {x}=p² {*} …(4) The equation (4) is in the algebraic form of the eigen value problem wherep is the eigen value and {x) is the eigen vector. The solution will give ‘n’ cigen values which will represent the squares of the ‘n’ natural’ frequencies of vibration and’n’ eigen vectors which will be the ‘n’ sets of normalised mode shapes.