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प्रश्न
A block of mass m is attached to two unstretched springs of spring constants k1 and k2 as shown in the following figure. The block is displaced towards the right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.
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उत्तर
The body is displaced x towards the right.
Let v be the velocity of the body at its mean position.
Applying the law of conservation of energy,
\[\frac{1}{2}\text{m} \nu^2 = \frac{1}{2} \text{k}_1 \text{x}^2 + \frac{1}{2} \text{k}_2 \text{x}^2\]
\[\Rightarrow \text{m} \nu^2 = \text{x}^2 \left( \text{k}_1 + \text{k}_2 \right)\]
\[ \Rightarrow \nu^2 = \frac{\text{x}^2 \left( \text{k}_1 + \text{k}_2 \right)}{m}\]
\[ \Rightarrow \nu = \text{x}\sqrt{\frac{\text{k}_1 + \text{k}_2}{\text{m}}}\]
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