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Physics-

General

Easy

Question

Two identical springs of constant $K$ are connected in series and parallel as shown in figure. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will be

2 :1
1 :1
1 :2
4 :1

The correct answer is: 1 :2

$n equals fraction numerator 1 over denominator 2 pi end fraction square root of fraction numerator K over denominator m end fraction end root rightwards double arrow fraction numerator n subscript S end subscript over denominator n subscript P end subscript end fraction equals square root of fraction numerator K subscript S end subscript over denominator K subscript P end subscript end fraction end root rightwards double arrow fraction numerator n subscript s end subscript over denominator n subscript p end subscript end fraction equals square root of fraction numerator open parentheses fraction numerator K over denominator 2 end fraction close parentheses over denominator 2 K end fraction end root equals fraction numerator 1 over denominator 2 end fraction$

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