A mass m performs oscillations of period T when hanged by spring of force constant K . If spring is

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13.Oscillations

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A mass m performs oscillations of period $T$ when hanged by spring of force constant $K$. If spring is cut in two parts and arranged in parallel and same mass is oscillated by them, then the new time period will be

A

$2T$

B

$T$

C

$\frac{T}{{\sqrt 2 }}$

D

$\frac{T}{2}$

Solution

(d) $T \propto \frac{1}{{\sqrt k }}$

==> $\frac{{{T_2}}}{{{T_1}}} = \sqrt {\frac{{{K_1}}}{{{K_2}}}} $$ = \sqrt {\frac{k}{{4k}}} = \frac{1}{2}$

==> ${T_2} = \frac{{{T_1}}}{2}$

Standard 11

Physics

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