A) \[2\pi \sqrt{\left( \frac{{{k}_{1}}+{{k}_{2}}}{m} \right)}\]
B) \[2\pi \sqrt{\left( \frac{m}{{{k}_{1}}+{{k}_{2}}} \right)}\]
C) \[2\pi \sqrt{\frac{m({{k}_{1}}{{k}_{2}})}{{{k}_{1}}+{{k}_{2}}}}\]
D) \[2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{({{k}_{1}}{{k}_{2}})}}\]
Correct Answer: D
Solution :
\[\frac{1}{k}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}\Rightarrow k=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]\[t=2\pi \frac{\sqrt{m({{k}_{1}}+{{k}_{2}})}}{{{k}_{1}}+{{k}_{2}}}\]
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