4.10 1mm mmmm mmm Three identical masses of mass m are connected by four identical springs of spring constant k between two rigid walls, as shown in the figure, and move without friction on a horizontal surface. They vibrate along the line joining their centres. (a) Show that the normal frequencies of the system are √2k/m and √(2±√2)k/m. (b) Describe the three normal modes of vibration. a11 12 13 [Hint: The determinant 421 422 423 431 432 433 (-23) + (azα13 - 033) +43 (012-2013).]