Two spring-mass systems support equal mass and have spring constants $K_{1}$ and $K_{2}$ . If the maximum velocities in two systems are equal then ratio of amplitude of 1st to that of 2nd is

\sqrt{K_{1} / K_{1}}

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K_{1} / K_{2}

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K_{2} / K_{1}

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\sqrt{K_{2} / K_{1}}

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Solution

The correct option is D $\sqrt{K_{2} / K_{1}}$
Maximum velocity $V_{m a x} = ω A$
$ω = \sqrt{\frac{K}{m}}$
$V_{1} = \sqrt{\frac{K_{1}}{m}} A_{1}$
$V_{2} = \sqrt{\frac{K_{2}}{m}} A_{2}$
It is given that both have same maximum velocity and same mass
$V_{1} = V_{2}$
$\sqrt{\frac{K_{1}}{m}} A_{1} = \sqrt{\frac{K_{2}}{m}} A_{2}$
$\frac{A_{1}}{A_{2}} = \sqrt{\frac{K_{2}}{K_{1}}}$

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