$\omega = \sqrt{\frac{k}{m}}$
$$\omega' = \sqrt{\frac{k/2}{2m}} = \sqrt{\frac{k}{4m}} = \frac{\omega}{2}$$
Verified 30 May 2026.
A spring-mass system oscillates with angular frequency $\omega$. If the mass is doubled and the spring constant is halved, the new angular frequency is:
$\frac{\omega}{2}$
$\frac{\omega}{\sqrt{2}}$
$2\omega$
$\omega\sqrt{2}$
$\omega = \sqrt{\frac{k}{m}}$
$$\omega' = \sqrt{\frac{k/2}{2m}} = \sqrt{\frac{k}{4m}} = \frac{\omega}{2}$$
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