A particle executes SHM starting from its mean position- at t -0 s- If it-s velocity is -3 b- when it is at a distance b from the mean position- where -2 -T- The time taken by the particle to move from b to the extreme position on the same side is A- -4 -B- -n-6 -C- -3 -D- -2 -

The correct option is C π/3ωv^2=ω^2(A^2 b^2) A^2=4b^2 implies b=A/2 From this, nbsp; A/2=Asin ω t nbsp; t=π/6ω Thus, required time is T/4 t=2π/4ω π/6ω= ...

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Byju's Answer

Standard XII

Physics

1st Equation of Motion

A particle ex...

Question

A particle executes SHM starting from its mean position, at $t = 0 s$ . If it's velocity is $\sqrt{3} b ω$ , when it is at a distance $b$ from the mean position, where $ω = \frac{2 π}{T}$ . The time taken by the particle to move from $b$ to the extreme position on the same side is

\frac{5 π}{6 ω}

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\frac{π}{3 ω}

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\frac{π}{2 ω}

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\frac{π}{4 ω}

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Solution

The correct option is B $\frac{π}{3 ω}$
$v^{2} = ω^{2} (A^{2} - b^{2})$
$⟹ A^{2} = 4 b^{2}$
$i m p l i e s b = A / 2$

From this,

$\frac{A}{2} = A s i n ω t ⟹ t = \frac{π}{6 ω}$

Thus, required time is $\frac{T}{4} - t = \frac{2 π}{4 ω} - \frac{π}{6 ω} = \frac{π}{3 ω}$

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A particle executes SHM starting from its mean position, at t=0s. If it's velocity is √3bω, when it is at a distance b from the mean position, where ω=2πT. The time taken by the particle to move from b to the extreme position on the same side is

The correct option is B π3ωv2=ω2(A2−b2) ⟹A2=4b2 impliesb=A/2 From this, A2=Asinωt⟹t=π6ω Thus, required time is T4−t=2π4ω−π6ω=π3ω

A particle executes SHM starting from its mean position, at $t = 0 s$ . If it's velocity is $\sqrt{3} b ω$ , when it is at a distance $b$ from the mean position, where $ω = \frac{2 π}{T}$ . The time taken by the particle to move from $b$ to the extreme position on the same side is

The correct option is B $\frac{π}{3 ω}$
$v^{2} = ω^{2} (A^{2} - b^{2})$
$⟹ A^{2} = 4 b^{2}$
$i m p l i e s b = A / 2$

From this,

$\frac{A}{2} = A s i n ω t ⟹ t = \frac{π}{6 ω}$

Thus, required time is $\frac{T}{4} - t = \frac{2 π}{4 ω} - \frac{π}{6 ω} = \frac{π}{3 ω}$