A disc of radius \(\text R\) is spun to an angular speed \(\omega\) about its axis and then imparted a horizontal velocity of magnitude \(\omega\text R/4\) at \(t = 0\) with its plane remaining vertical.

The coefficient of friction between the disc and the plane is \(\mu\). The sense of rotation is anticlockwise and linear speed is in forward direction. Find the time taken by the disc to return to its initial point.

**Details and Assumptions:**

If your answer is \(\text T\). Then define \(f = \mu g\text T/\omega R\), where \(g\) is the acceleration due to Gravity on earth.

If \(f = a/b\) for positive co-prime integers \(a,b\).

Find the value of \(a+b\).

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