A block of mass m is attached to two unstretched springs of spring constants $k_{1}$ and $k_{2}$ as shown in figure.The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.

\sqrt{\frac{k_{1} + k_{2}}{m}} x

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\sqrt{\frac{k_{1} k_{2}}{m (k_{1} + k_{2})}} x

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\sqrt{\frac{k_{1}^{2} k_{2}^{2}}{m (k_{1}^{2} + k_{2}^{2})}} x

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\sqrt{\frac{k_{1}^{3} k_{2}^{3}}{m (k_{1}^{3} + k_{2}^{3})}}

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Solution

The correct option is A $\sqrt{\frac{k_{1} + k_{2}}{m}} x$
$\frac{1}{2} k_{1} x^{2} + \frac{1}{2} k_{2} x^{2} = \frac{1}{2} m v^{2}$
$v^{2} = \frac{k_{1} + k_{2}}{m} x^{2}$
$v = \sqrt{\frac{k_{1} + k_{2}}{m}} x$

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Figure

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A block of mass m is attached to two unstretched springs of spring constants k1 and k2 as shown in figure.The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.

The correct option is A √k1+k2mx12k1x2+12k2x2=12mv2v2=k1+k2mx2v=√k1+k2mx

A block of mass m is attached to two unstretched springs of spring constants $k_{1}$ and $k_{2}$ as shown in figure.The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.

The correct option is A $\sqrt{\frac{k_{1} + k_{2}}{m}} x$
$\frac{1}{2} k_{1} x^{2} + \frac{1}{2} k_{2} x^{2} = \frac{1}{2} m v^{2}$
$v^{2} = \frac{k_{1} + k_{2}}{m} x^{2}$
$v = \sqrt{\frac{k_{1} + k_{2}}{m}} x$