Problem 2 (2.5%) An arbitrary bar of mass $m$ and radius of gyration $\kappa$ with respect to its center of
gravity is suspended horizontally by two strings of length $h$ as shown below. The distance from the
center of gravity to the string on the left is $a$, and that to the string on the right is $b$.
1. (0.5%) What are the tensions inside these strings?
2. (1.0%) Derive the equation of motion of this bar rotating about the vertical axis passing through
the center of gravity.
3. (1.0%) Determine the natural frequency of rotating motion in terms of $a$, $b$, $h$, $\kappa$ and gravity $g$.
