A body of mass 1 kg is executing simple harmonic motion. Its displacement x (in cm) at time t (in second) is given by
$x = 6 s i n (100 t + \frac{π}{4})$ The maximum kinetic energy of the body is

6 J

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18 J

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24 J

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36 J

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Solution

The correct option is B 18 J
Velocity of the body at time t is
$v = \frac{d x}{d t} = (6 \times 100) c o s (100 t + \frac{π}{4}) c m s^{- 1}$
$∴ V_{m a x} = 600 c m s^{- 1} = 6 m s^{- 1}$
Maximum KE $\frac{1}{2} m v_{m a x}^{2} = \frac{1}{2} \times 1 \times (6)^{2} = 18 J$
Hence the correct choice is (b)

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