The time period of oscillation for the given | vedclass

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(A) In the given figure,the two springs with spring constants $K_{1}$ and $K_{2}$ are connected in series.The equivalent spring constant $K_{eq}$ for

Vedclass · Accepted Answer

$2 \pi \sqrt{\frac{m(K_{1}+K_{2})}{K_{1}K_{2}}}$

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(A) In the given figure,the two springs with spring constants $K_{1}$ and $K_{2}$ are connected in series.The equivalent spring constant $K_{eq}$ for springs in series is given by the formula:$\frac{1}{K_{eq}} = \frac{1}{K_{1}} + \frac{1}{K_{2}}$Solving for $K_{eq}$:$K_{eq} = \frac{K_{1}K_{2}}{K_{1}+K_{2}}$The time period $T$ of oscillation for a mass $m$ attached to a spring system is given by:$T = 2 \pi \sqrt{\frac{m}{K_{eq}}}$Substituting the value of $K_{eq}$:$T = 2 \pi \sqrt{\frac{m}{\left(\frac{K_{1}K_{2}}{K_{1}+K_{2}}\right)}}$$T = 2 \pi \sqrt{\frac{m(K_{1}+K_{2})}{K_{1}K_{2}}}$

The time period of oscillation for the given combination will be:

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