Frequency of oscillations of a mass m connected horizontally by a spring of spring constant k is 4 H

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13.Oscillations

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The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 Hz$. When the spring is replaced by two identical spring as shown in figure. Then the effective frequency is,

A

$4 \sqrt{2}$

B

$1.5$

C

$1.31$

D

$2 \sqrt{2}$

(AIIMS-2016)

Solution

(d)

in series $k_{e q}=\frac{k \times k}{k+k}=\frac{k^2}{2 k}=\frac{k}{2}$

$\therefore \omega \sqrt{\frac{k e r}{m}}=\sqrt{\frac{k}{m}} \times \frac{1}{\sqrt{2}}$

$\text { and } \sqrt{\frac{k}{m}}=4$

$\text { effective frequency }=\frac{4}{\sqrt{2}}=2 \sqrt{2}$

Standard 11

Physics

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