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A particle executes S.H.M. with amplitud...

A particle executes S.H.M. with amplitude 'a' and time period T. The displacement of the particle when its speed is half of maximum speed is `(sqrt(x)a)/(2)`. The value of x is ………… .

Text Solution

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The correct Answer is:
3
For a particle executes S.H.M
`v = omega sqrt( a^(2) - x^(2))`
Given ` v = (v_("max"))/( 2) rArr (a omega)/( 2)`
` (a^(2) omega ^(2))/( 4) = omega ^(2) a^(2) - omega ^(2) x^(2)`
`x = (sqrt(3))/( 2) a `
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