It is said that:
$$ F = -m\omega^2 x = -kx, $$
so $k=m\omega^2$. Since $k$ is the spring constant it doesn't depend on the mass of the object attached to it, but here $m$ signifies the mass of the object. Then how is $k$ independent of the mass attached?
Best Answer
$\omega$ isn't a constant of the spring, but it actually depends on the mass you attach to the spring. $\omega$ refers to the frequency of oscillation of the attached mass. The formula for $\omega$ for an attached mass $m$ is $\sqrt{\frac{k}{m}}$, where $k$ is the spring constant. If you use $\omega=\sqrt{\frac{k}{m}}$ in the formula, $m$ cancels out leaving only $k$