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Physics-

General

Easy

Question

In the figure, $S subscript 1 end subscript$ and $S subscript 2 end subscript$ are identical springs. The oscillation frequency of the mass $m$ is $f.$ If one spring is removed, the frequency will become

$f$
$f \times 2$
$f \times \sqrt{2}$
$f / \sqrt{2}$

The correct answer is: $f divided by square root of 2$

For the given figure $f equals fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator k subscript e q end subscript over denominator m end fraction end root equals fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator 2 k over denominator m end fraction end root$ (i)
If one spring is removed, then $k subscript e q end subscript equals k$ and
$f to the power of ´ end exponent equals fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator k over denominator m end fraction end root blank left parenthesis i i right parenthesis$
From equation (i) and (ii),
$fraction numerator f over denominator f to the power of ´ end exponent end fraction equals square root of 2 rightwards double arrow f to the power of ´ end exponent equals fraction numerator f over denominator square root of 2 end fraction$

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