3. Three coupled pendulums swing perpendicularly to the horizontal line contain- ing their points of suspension, and the following equations of motion are satisfied: m1 = cmX1+d(X1 X2 ), -MX = cMx2 + d(x2 x1) + d(x2 x3), -mx3 = cmx3 + d(x3 x), where x, x and x3 are measured from the equilibrium points; m, M and m are the masses of the pendulum bobs; and c and d are positive constants. Find the normal frequencies of the system and sketch the corresponding patterns of oscillation.