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A particle executes simple harmonic motion with an amplitude of .At the mean position the velocity of the particle is . The distance of the particle from the mean position when its speed becomes is:

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answer is C.

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Detailed Solution

Concept: A particle oscillates harmonically simply with amplitude a. The oscillation's period is T. The particle must move half the amplitude from the equilibrium point in the least amount of time possible.
Given,
Amplitude,

velocity of the particle at mean position,

We know the relation between speed of particle, amplitude and distance of particle from mean position is given by,

Here

is angular frequency,
speed at mean position,

speed at

distance from mean position,

Hence, the correct option is 3.

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