Circular Motion

A particle is moving in a circle of radius \(50 \mathrm{~cm}\) in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at \(\mathrm{t}=0\) is \(4 \mathrm{~m} / \mathrm{s}\), the time taken to complete the first revolution will be \(\frac{1}{\alpha}\left[1-e^{-2 \pi}\right] \mathrm{s}\), where \(\alpha=\) _________.