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A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L=0.5m and the mass of attached bob m=2kg, the stiffness coefficient of the connecting spring is k=80Ns/m. a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form [1 0][??1] + [g/L + k/m -k/m][?1] = 0 [0 1][??2] [-k/m g/L + k/m][?2] b) Using the characteristic equation method or transformation to principal coordinates find out two frequencies and modes of oscillation for the system of coupled pendulums in Figure A2 c) Describe the method of exciting separately each mode of vibration

          A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L=0.5m and the mass of attached bob m=2kg, the stiffness coefficient of the connecting spring is k=80Ns/m.

a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form

[1 0][??1] + [g/L + k/m  -k/m][?1] = 0
[0 1][??2]   [-k/m  g/L + k/m][?2]

b) Using the characteristic equation method or transformation to principal coordinates find out two frequencies and modes of oscillation for the system of coupled pendulums in Figure A2
c) Describe the method of exciting separately each mode of vibration

A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L=0.5m and the mass of attached bob m=2kg, the stiffness coefficient of the connecting spring is k=80Ns/m.

a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form

[1 0][??1] + [g/L + k/m -k/m][?1] = 0
[0 1][??2] [-k/m g/L + k/m][?2]

b) Using the characteristic equation method or transformation to principal coordinates find out two frequencies and modes of oscillation for the system of coupled pendulums in Figure A2
c) Describe the method of exciting separately each mode of vibration

Added by Erica J.

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