First slide

Simple hormonic motion

Question

A particle starts s with S.H.M. from the mean position . Its amplitude is A and its time periods T, At one time, its speed is half that of the maximum speed. What is thie distance of the particle from mean position at that instant ?

Moderate

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

we know that v $= ω {[A^{2} - x^{2}]}^{1 / 2}$
$X = {[A^{2} - \frac{V^{2}}{ω^{2}}]}^{1 / 2} Given that V = \frac{Aω}{2} so X = {[A^{2} - \frac{A^{2} ω^{2}}{4 ω^{2}}]}^{1 / 2} = \frac{\sqrt{3}}{2} \cdot A$

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