To make the frequency double of an oscillator, we have to
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$\omega = \sqrt {\frac{k}{m}} $
$\Rightarrow \frac{{{\omega _2}}}{{{\omega _1}}} = \sqrt {\frac{{{m_1}}}{{{m_2}}}} $
$\Rightarrow 2 = \sqrt {\frac{{{m_1}}}{{{m_2}}}} $
$\Rightarrow {m_2} = \frac{{{m_1}}}{4}$
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