Question

9. A mechanical component can be modelled as a pendulum with a torsional damper of coefficient, c, at its oO hinge as shown in Figure Q.9. Stiffness in the system is modelled by a spring of stiffness, k, located at the midpoint of the light bar of length 1. The pendulum is free to rotate about the hinge O and has bob-mass m a) Show that the equation of motion of the system for small angular displacements, 6, is given by: ml2 b) The values of the damping and stiffness of the system are to be obtained by experiment. The damper is removed, and it is noted that in free vibration the pendulum completes 5 oscillations in 4 seconds. The damper iS reconnected and in free vibration it is noted that the oscillations decay to 10% of the initial Figure Q.9 ENG3039 - Tutorial 1 : Page 4 displacement in 3 complete oscillations. Given that m 5kg and l 1m determine the values of k and o c) Using the values calculated in b), derive an expression for the free vibration of the system in response to an initial angular displacement, 0o.

Answer 1