After losing the metre stick the lab instructor begins to oscillate a disc attached to a piece of wire.

The disc weighs $500$ g and has a radius of $15$ cm and a thickness of $2$ cm$.$ The wire is made of$\mathrm{ 7}072$ aluminum and has a length of $20\mathrm{.}2$ cm and a radius of $3$ mm$.$ What is the oscillatory period?