QUIZ 1Two pendula pivot about an axisAand are constrained to remain in planesperpendicular to that axis. Furthermore the pivot points remain fixed. Each has alengthLand a massm. The angles from the vertical are θ1and θ2. (In the pictureθ1<0 and θ2>0). The two pendula are coupled by a weak torsional spring that obeysHooke's Law with torsional spring constant κτ2=−κ θ2−θ1()=−τ1where τ2is the torque on mass 2 and τ1is the torque on mass 1.(a) [2.5 pts] Write down the linear coupled differential equations describing themotion of the pendula when the anglesθi1.(b) [2.5 pts] Find the two normal‐mode frequencies (eigenfrequencies).
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