Question

The natural frequency of a spring-mass system on earth is ${\omega }_n$. The natural frequency of this system on the moon $g_{moon}=g_{earth}/6$ is

• A. ${\omega }_n$
• B. 0.408 ${\omega }_n$
• C. 0.204${\omega }_n$
• D. 0.167${\omega }_n$

Answer 1

The correct option is A ${\omega }_n$

As we know that, ${\omega }_n$ doesn't depend on gravity, it depends on the mass
${\omega }_n\propto \frac{1}{\sqrt{m}}$

And again,
${\omega }_n=\sqrt{\frac{g}{\delta }}$

Since it is a spring mass-system,
$\delta =\frac{mg}{k}$

${\omega }_n=\sqrt{\frac{g}{\frac{mg}{k}}}=\sqrt{\frac{k}{m}}$

So, ${\omega }_n$ will be constant everywhere.