A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius \( R=4~\mbox{cm}\). The plane of the coin is tilted at an angle of \(\theta=45^{\circ}\) with respect to the horizontal plane (see the figure below). Find the coin's period \(T\) **in seconds**, that is, the time it takes for the coin to go around the circle of radius \(R\). The radius of a U.S quarter is \(r=1.2 ~\mbox{cm}\).

**Details and assumptions**

Assume \(g=9.8~\mbox{m/s}^{2}\).

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