An object of mass 3 kg is executing simple harmonic motion with an amplitude $\frac{2}{π} m$ . If the kinetic energy of the object when it crosses the mean position is 6 J, the time period of oscillation of the object is

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4 s

3 s

1 s

2 s

answer is B.

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Detailed Solution

The kinetic energy at the mean point is given by $K = \frac{1}{2} m A^{2} ω^{2} = \frac{1}{2} \times 3 \times {(\frac{2}{π})}^{2} \times (\frac{4 π^{2}}{T^{2}}) = 6$

$\Rightarrow T = 2 s$

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