$\mathrm{v}=\frac{\mathrm{d} \mathrm{x}}{\mathrm{dt}}=\mathrm{A} \omega \cos \omega \mathrm{t}=\omega \sqrt{\mathrm{A}^{2}-\mathrm{x}^{2}}$

$\mathrm{a}=\frac{\mathrm{d} \mathrm{v}}{\mathrm{dt}}=-\mathrm{A} \omega^{2} \sin \omega \mathrm{t}$

$\mathrm{a}=\frac{\mathrm{d} \mathrm{v}}{\mathrm{dt}}=-\omega^{2} \mathrm{x}$

But $x=-\frac{a}{\omega^{2}}$

$\therefore \quad v=\omega \sqrt{A^{2}-\frac{a^{2}}{\omega^{4}}}$

or $v^{2}=\omega^{2}\left(A^{2}-\frac{a^{2}}{\omega^{4}}\right)$