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The displacement of a particle executing SHM is given by $y = 5 \sin (4 t + \frac{π}{3}) m$ . If T is the time period and the mass of the particle is 2 gm the kinetic energy of the particle when $t = \frac{T}{4}$ is given by

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0.3 J

0.4 J

0.5 J

0.6 J

answer is A.

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Detailed Solution

From $y = 5 \sin (4 t + \frac{π}{3})$ here $ω = 4 r a d s^{- 1}$

$∴ T = \frac{2 π}{ω} = \frac{π}{2} \sec$

When

$t = \frac{T}{4}, y = 5 \sin (\frac{π}{2} + \frac{π}{3}) = (\cos \frac{π}{3}) 5 = 2.5 m$

$K t = \frac{1}{2} m ω^{2} (A^{2} - y^{2}) = \frac{1}{2}$

$[{(5)}^{2} - {(2.5)}^{2}]$

$∴ K E = 0.3 J$

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