(Solved): A large compound pendulum is to be used as a tuned mass damper to suppress the oscillations of a s ...

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 \( 0.65 \mathrm{~Hz} \) The required length of the pendulum can be calculated using the following equation (adapted from Practical Engineering 3): The pendulum rod has a length of \( 2 \mathrm{~m} \) and a mass of \( 400 \mathrm{~g} \), and there are three masses available to be used as the bob: \[ \begin{array}{l} m_{1}=2.5 \mathrm{~kg} \\ m_{2}=3.0 \mathrm{~kg} \\ m_{3}=3.5 \mathrm{~kg} \end{array} \] a The engineers would like to minimise the mass of the bob. Which of the three masses should they use for the bob? Justify your answer. 3 marks b For the mass you identified, use the equation to calculate \( L \), the distance from the pin to the centre of mass of the bob'. Give your answer to two significant figures. 2 marks c. Identify one approximation used in deriving the equation and suggest if this is