A particle starts SHM from the mean position. Its amplitude is A and its time period is T. At sometime, its speed is half that of the maximum speed. Displacement of the particle at this instant is:

A particle starts SHM from the mean position. Its amplitude is A and its time period is T. At sometime, its speed is half that of the maximum speed. Displacement of the particle at this instant is:

A
$\frac{\sqrt{2} A}{3}$
B
$\frac{\sqrt{3} A}{2}$
C
$\frac{2 A}{\sqrt{3}}$
D
$\frac{3 A}{\sqrt{2}}$

Solution:

Speed, $ω \sqrt{A^{2} - x^{2}} = \frac{1}{2} Aω \Rightarrow x = \frac{\sqrt{3}}{2} A$

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