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A particle starts with S.H.M. from the m...

A particle starts with S.H.M. from the mean position as shown in the figure. Its amplitude is A and its time period is T. At any instant, its speed is half that of the maximum speed. What is the displacement of the particle at the that point?

A

`(2A)/sqrt(3)`

B

`(3A)/sqrt(2)`

C

`(sqrt(2)A)/3`

D

`(sqrt(3)A)/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Maximum velocity `v_("max") = Aomega`
According to question, `v_("max")/2 = (Aomega)/2 = omega sqrt(A^(2) -y^(2))`
`A^(2)/4 = A^(2) -y^(2) rArr y^(2) = A^(2) -A^(2)/4 rArr y=(sqrt(3)A)/2`
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