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

Q: 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

b (b) 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 $y' = y\cos 45^\circ .$ So that the total restoring force on the mass $m $ along $ OA.$ ${F_{net}} = {F_A} + {F_B}\cos 45^\circ + {F_C}\cos 45^\circ $ $ = ky + 2ky'\cos 45^\circ $$ = ky + 2k(y\cos 45^\circ )\cos 45^\circ $$ = 2ky$ Also ${F_{net}} = k'y$ ==> $k'y = 2ky$==> $k' = 2k$ $T = 2\pi \sqrt {\frac{m}{{k'}}} = 2\pi \sqrt {\frac{m}{{2k}}} $

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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

A$2\pi \sqrt {\frac{{2m}}{k}} $
B$2\pi \sqrt {\frac{m}{{2k}}} $
C$2\pi \sqrt {\frac{m}{k}} $
D$2\pi \sqrt {\frac{m}{{3k}}} $

Diffcult

STD 11 Science
NEET
STD 11 - 13. oscillations
Physics

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