The time-period of oscillations of the springs is
A) \[T=\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}\]
B) \[T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}\]
C) \[T=2\pi \sqrt{\frac{m}{{{k}_{1}}+{{k}_{2}}}}\]
D) \[T=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{2{{k}_{1}}{{k}_{2}}}}\]
Correct Answer: B
Solution :
In series combination spring constants of combination \[\frac{1}{{{k}_{s}}}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}\] \[\Rightarrow \] \[{{k}_{s}}=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\] Time period of combination \[T=2\pi \sqrt{\frac{m}{{{k}_{s}}}}=2\pi \sqrt{\frac{m({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}}\]
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