A) \[T=2\pi \sqrt{\left( \frac{m}{{{K}_{1}}+{{K}_{2}}} \right)}\]
B) \[T=2\pi \sqrt{\left( \frac{m}{{{K}_{1}}+{{K}_{2}}} \right)}\]
C) \[T=2\pi \sqrt{\left( \frac{m({{K}_{1}}+{{K}_{2}})}{{{K}_{1}}{{K}_{2}}} \right)}\]
D) \[T=2\pi \sqrt{\left( \frac{m{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)}\]
Correct Answer: C
Solution :
In series \[{{k}_{eq}}=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]so time period \[T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}\]
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