A particle executes simple harmonic motion with an amplitude of 4cm...

The formula to calculate the velocity of the particle at the mean position is given by

$V = A\omega . . . \left(1\right)$

From equation (1), it follows that

$10 = 4 \times \omega ⇒ \omega = \dfrac{5}{2}rad{s}^{- 1}$

The formula to calculate the velocity of the particle at any instantaneous position $x$ can be expressed as

$v = \omega\sqrt{{A}^{2} - {x}^{2}} . . . \left(2\right)$

From equation (2), it follows that

$5 = \dfrac{5}{2}\sqrt{{4}^{2} - {x}^{2}} ⇒ {x}^{2} = 16 - 4 = 12 ⇒ x = \sqrt{12}cm$

Hence, $\alpha = 12$.