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Physics-

General

Easy

Question

A particle of mass m is attached to three identical springs A, 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 $y to the power of ´ end exponent equals y cos invisible function application 4 5 degree.$ So that the total restoring force on the mass m along OA.

$F subscript n e t end subscript equals F subscript A end subscript plus F subscript B end subscript cos invisible function application 4 5 degree plus F subscript C end subscript cos invisible function application 4 5 degree$
$equals k y plus 2 k y to the power of ´ end exponent cos invisible function application 4 5 degree equals k y plus 2 k left parenthesis y cos invisible function application 4 5 degree right parenthesis cos invisible function application 4 5 degree equals 2 k y$
Also $F subscript n e t end subscript equals k to the power of ´ end exponent y$ Þ $k to the power of ´ end exponent y equals 2 k y$ Þ $k to the power of ´ end exponent equals 2 k$
$T equals 2 pi square root of fraction numerator m over denominator k to the power of ´ end exponent end fraction end root equals 2 pi square root of fraction numerator m over denominator 2 k end fraction end root$

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