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Paragraph : A particle vibrates in S.H.M. along a straight line. Its velocity is 4 cm/s when its displacement is 3 cm and velocity is 3 cm/s when displacement is 4 cm. Starting from origin a body oscillates simple harmonically with a period of 2 s. After what time will its kineti energy be 75% of the total energy. |
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Answer» `(1)/(6)s` `implies(1)/(2)m OMEGA^(2)(R^(2)-y^(2))=(3)/(4)((1)/(2)m omega^(2)r^(2))` `r^(2)-y^(2)=(3)/(4)r^(2)""impliesy=r//2` Now `y=r sin omegatimplies( r )/(2)=r sin" wt"impliessin omegat=(1)/(2)` `implies""omegat=pi//6""implies(2pi)/(T)t=(pi)/(6)""implies""t=(T)/(12)` So CORRECT choice is (a). |
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