The natural frequency f of vibration of a mass M attached to a rod, depends

only on the mass M attached to the rod and the stiffness EI and length L of the rod. Tests

with a $2$ kg mass attached to a $1040$ carbon steel rod of diameter $12$ mm and length $40$ cm

$($EI$=2\mathrm{.}05$ x$10^11*($pi$)*(0\mathrm{.}006^4)/4$ kg m$3/$s$2)$ reveal a natural frequency of $0\mathrm{.}9$ Hz$.$ Use this result

to predict the natural frequency in Hertz for a $0\mathrm{.}8$ kg mass attached to a square $2024$

aluminum bar $12$ mm on a side and $38$ centimeters long

$($EI$=7\mathrm{.}3$ x$10^10*(0\mathrm{.}012^4)/12$ kg m$3/$s$2).$

$($hint: use Dimensional analysis$)$