Writing $w_b$ in terms of $w_a$

Question

Blanking out on this.. if I have $w_a = \sqrt{\frac km}$ and $w_b = \sqrt{\frac k{2m}}$, how can i rewrite $w_b$ in terms of $w_a$? Would it just be $\frac1{\sqrt2}\sqrt{\frac km}$?

Answer 1

$w_a=\sqrt{\frac{k}{m}}$ and $w_b=\sqrt{\frac{k}{2m}}$

But $w_b=\sqrt{\frac{k}{2m}}=\frac{\sqrt{k}}{\sqrt{2}\times\sqrt{m}}=\frac{1}{\sqrt{2}}\times\sqrt{\frac{k}{m}}=\frac{1}{\sqrt{2}}m_a$

So you are right.