Please answer in detail with every step.

5-7 Two objects, A and B. each of mass m, are connected by Spring as shown. The coupling spring has a spring constant kg, and the other two springs have spring constant k0. If Bis clamped, A vibrates at a frequency :5. of 1.81sec". The frequency in of the lower normal mode is 1.14 sec". 2 A 3 g ft\" m t. m L. x; (a) Satisfy yourself that the equatEOns of motion of A and B are 2 \"1% = koxA - hora - x3) 61ng m = -koxa - kc(xa - x4) ([3) Putting wg = Vito/m, show that the angular frequencies on and :92 of the normal modes are given by 0:1 = :00, we = [me2 + (ch/M)l"2, and that the angular frequency of A when Bis clamped (x3 = 0 always) is given by m = [me2 + (kc/"01m (c) Using the numerical data above, calculate the expected frequency (v2) of the higher normal mode. (The observed value was 2.27 sec'.) (d) From these same data calculate the ratio (cf/kn of the two spring constants