A mass m is suspended by means of two coiled spring which have same length in unstretched condition

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13.Oscillations

easy

A mass $m$ is suspended by means of two coiled spring which have the same length in unstretched condition as in figure. Their force constant are $k_1$ and $k_2$ respectively. When set into vertical vibrations, the period will be

A

$2\pi \sqrt {\left( {\frac{m}{{{k_1}{k_2}}}} \right)} $

B

$2\pi \sqrt {m\left( {\frac{{{k_1}}}{{{k_2}}}} \right)} $

C

$2\pi \sqrt {\left( {\frac{m}{{{k_1} - {k_2}}}} \right)} $

D

$2\pi \sqrt {\left( {\frac{m}{{{k_1} + {k_2}}}} \right)} $

Solution

(d) Given spring system has parallel combination, so
${k_{eq}} = {k_1} + {k_2}$ and time period $T = 2\pi \sqrt {\frac{m}{{({k_1} + {k_2})}}} $

Standard 11

Physics

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