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Physics-

General

Easy

Question

A particle of mass $m$ is attached to three identical springs $A comma blank B$ and $C$ each of force constant $k$ a shown in figure. If the particle of mass $m$ is pushed slightly against the spring $A$ and released then the time period of oscillations is

$2 π \sqrt{\frac{2 m}{k}}$
$2 π \sqrt{\frac{m}{2 k}}$
$2 π \sqrt{\frac{m}{k}}$
$2 π \sqrt{\frac{m}{3 k}}$

The correct answer is: $2 pi square root of fraction numerator m over denominator 2 k end fraction end root$

When the particle of mass $m$ at $O$ is pushed by $y$ in the direction of $A$ the spring $A$ will be compressed by $y$ while spring $B$ and $C$ will be stretched by $y to the power of ´ end exponent equals y cos invisible function application 45 degree$ .So that the total restoring force on the mass $m$ along $O A$

$F subscript n e t end subscript equals F subscript A end subscript plus F subscript B end subscript cos invisible function application 45 degree plus F subscript C end subscript cos invisible function application 45 degree$
$equals k y plus 2 k y to the power of ´ end exponent cos invisible function application 45 degree equals k y plus 2 k open parentheses y cos invisible function application 45 degree close parentheses cos invisible function application 45 degree equals 2 k y$
Also $F subscript n e t end subscript equals k to the power of ´ end exponent y rightwards double arrow k to the power of ´ end exponent y equals 2 k y rightwards double arrow k to the power of ´ end exponent equals 2 k$
$T equals 2 pi square root of fraction numerator m over denominator k to the power of ´ end exponent end fraction end root equals 2 pi square root of fraction numerator m over denominator 2 k end fraction end root$

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