Question: A large compound pendulum is to be used as a tuned mass damper to suppress the oscillations of a structure with a natural frequency

A large compound pendulum is to be used as a tuned mass damper to suppress the oscillations of a structure with a natural frequency of 0.50 Hz. From Practical Engineering 3, the required length of the pendulum can be calculated using the following equation: Lbob = 12 2 + (+) - mrod! 4 - 17 bob 3 g 2w2 The pendulum rod has a length of 2.8 m and a mass of 2 kg, and there are four masses available to be used as the bob: m1 = 8.0 kg m2 10.0 kg = m3 = m4 = 12.0 kg 14.0 kg a. The engineers would like to minimise the mass of the bob. Which of the four masses should they use for the bob? Justify your answer. 3 marks b. For the mass you identified use the equation to calculate Lbob, the distance from the pin to the centre of mass of the bob. Give your answer to two significant figures 2 marks c. If the mass of the rod is negligible compared to the mass of the bob, show that the equation for Lbob is consistent with the equation for a simple pendulum: 1 9 f 2T 2 marks

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