A) \[T=2\pi \sqrt{\frac{m}{{{k}_{1}}+{{k}_{2}}}}\]
B) \[T=2\pi \sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{m}}\]
C) \[T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}+{{k}_{2}}}}\]
D) \[T=2\pi \sqrt{\frac{mg}{{{k}_{1}}+{{k}_{2}}}}\]
Correct Answer: A
Solution :
Key Idea: The two springs in figure are in parallel. The periodic time of spring-mass system is \[T=2\pi \sqrt{\frac{m}{k}}\] In the given case the combined force constant springs are in parallel, is \[k={{k}_{1}}+{{k}_{2}}\] \[\therefore \] \[T=2\pi \sqrt{\frac{m}{{{k}_{1}}+{{k}_{2}}}}\]
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