Two 2 × 2 matrices with real entries are given below:

(a) State the conditions on the entries of M under which it can represent the massmatrix of a two-degree-of-freedom mechanical system.

(b) State the conditions on the entries of K under which it can represent the stiffnessmatrix of a two-degree-of-freedom mechanical system. Here, allow for thepossibility of rigid modes.

(c) We now assume that

are the mass and the stiffness matrices of a certain two-degree-of-freedommechanical system. Find its natural frequencies and its natural modes.

Transcribed Image Text:

M = [a b] [c d] K= e gh