Required information

A $\backslash (15-\backslash$mathrm$\{$lb$\}\backslash )$ slender rod $\backslash ($ A B $\backslash )$ is riveted to a $\backslash (12-\backslash$mathrm$\{$lb$\}\backslash )$ uniform disk as shown. A belt is attached to the rim of the disk and to a spring that holds the rod at rest in the position shown. End $\backslash ($ A $\backslash )$ of the rod is moved $0\mathrm{.}75$ in $.$ down and released. The value of the spring constant is $\backslash ($ k$=75\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$in$\}\backslash ).$

Determine the period of vibration. $($Round the final answer to three decimal places.$)$

The period of vibration is