The bell-crank mechanism consists of a bent rod and an attached 5-kg weight. The rod has negligible weight, and the mass has negligible size. The weight is deflected slightly and released. The ensuing angular oscillations are monitored, and a shaft encoder provides the position data shown in the diagram where the time scale (in second) is calibrated but the position scale is not (meaning that we do not know the value of a unit).
Note: Only part (e) requires the answer to part (a). Parts (b), (c) and (d) can be done without (a). The grading for part (e) will be based on your answer in part (a), so as not to mark down twice for errors in part (a).
a) Using Newton's laws, find the equation of motion.
b) Find the damped natural frequency.
c) Find the damping factor.
d) Find the undamped natural frequency.
e) Find the spring constant, k and damping coefficient.