A $2\mathrm{.}00$ m$-$long $6\mathrm{.}00-$kg ladder pivoted at the top hangs down from a platform at the circus. A $42\mathrm{.}0-$kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the system's natural frequency. The angular frequency $($in s$1)$ of the system of ladder and woman is

Question $8$ options:

a$)$

$4\mathrm{.}03.$

b$)$

$16\mathrm{.}2.$

c$)$

$8\mathrm{.}05.$

d$)$

$1\mathrm{.}01.$

e$)$

$3\mathrm{.}07.$