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Standard XII

Physics

Waves of Sound

Two particles...

Question

Two particles $A$ and $B$ of eqaul masses are suspended from two massless springs of spring constants $K_{1}$ and $K_{2}$ respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of $A$ and $B$ is :

\sqrt{\frac{K_{2}}{K_{1}}}

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\sqrt{\frac{K_{1}}{K_{2}}}

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\frac{K_{2}}{K_{1}}

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\frac{K_{1}}{K_{2}}

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Solution

The correct option is A $\sqrt{\frac{K_{2}}{K_{1}}}$
We know that, maximum speed: $V_{m a x} = A ω$ Given: $ω_{1} A_{1} = ω_{2} A_{2}$

We know that $ω = \sqrt{\frac{K}{m}}$

$\Rightarrow \sqrt{\frac{K_{1}}{m}} A_{1} = \sqrt{\frac{K_{2}}{m}} A_{2}$

$∴ \frac{A_{1}}{A_{2}} = \sqrt{\frac{K_{2}}{K_{1}}}$

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