A particle executes simple harmonic motion with an amplitude of \( 4 \, \text{cm} \). At the mean position, velocity of the particle is \( 10 \, \text{cm/s} \). The distance of the particle from the mean position when its speed becomes \( 5 \, \text{cm/s} \) is \( \sqrt{\alpha} \, \text{cm} \), where \( \alpha = \) ______________.
