Answer Happy

Question 8 (Unit 11) - 6 marks The oscillations of three particles A, B and C are governed by the matrix equation lä 7- 11 ü = 1 -3 2 y , z) 0 1 -1) where x, y and z are the particles' respective displacements from equilibrium. (a) Show that the vector (0.5 -2.87 1)T is an approximate eigenvector of the dynamic matrix (to two decimal place accuracy) by calculating the corresponding eigenvalue. (b) Calculate the corresponding normal mode angular frequency for the normal mode with the given normal mode eigenvector. (c) Give an initial displacement vector that would lead to the normal mode motion corresponding to the given eigenvector. (d) For this normal mode motion, state (with a reason which of the particles are moving in phase.