3. Three coupled pendulums swing perpendicularly to the horizontal line contain- ing their points of suspension,...
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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 ), -MX₂ = cMx2 + d(x2 − x1) + d(x2 − x3), -mx3 = cmx3 + d(x3 − x₂), where x₁, x₂ 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. 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 ), -MX₂ = cMx2 + d(x2 − x1) + d(x2 − x3), -mx3 = cmx3 + d(x3 − x₂), where x₁, x₂ 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.
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