An Introduction to Matrix Formalism for Two Masses

The general case of two masses bound by two lateral springs k and L2, and coupled by a coupling spring, in Fig. 5-2b, has 

The rules of matrix-vector multiplication show that the matrix form is the same as the algebraic form, Eq. (5-25) 

Interest now centers on the matr ix K. Equation (5-26) is general, but to introduce the method, let all spr ings have the same force constant. We have the matr ix arising from the equations of motion. 

If the coupling spring is missing [k = 0 in Eq. (5-28)], we get a unique diagonal matrix 

Because the masses are the same, these equations describe independent oscillators with identical frequencies, as in Fig. 5-la. 

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