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The equation for the displacement of a particle executing SHM is $y = \{5 \sin 2 πt\} cm .$ Find (i) the velocity at 3 cm from the mean position, (ii) acceleration after 0.5s after leaving the mean position.

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$8 {πcms}^{- 1}, zero$

$6 {πcms}^{- 1}, zero$

$4 {πcms}^{- 1}, zero$

$2 {πcms}^{- 1}, zero$

answer is A.

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Detailed Solution

$V = ω \sqrt{A^{2} - Y^{2}} = 2 π \sqrt{5^{2} - 3^{2}} = 8 πcm / s .$

$a = - ω^{2} y$

$when t = 2 \sec y = 0$

$a = 0$

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