A) \[2\pi \sqrt{\left( \frac{m}{{{k}_{1}}{{k}_{2}}} \right)}\]
B) \[2\pi \sqrt{m\left( \frac{{{k}_{1}}}{{{k}_{2}}} \right)}\]
C) \[2\pi \sqrt{\left( \frac{m}{{{k}_{1}}-{{k}_{2}}} \right)}\]
D) \[2\pi \sqrt{\left( \frac{m}{{{k}_{1}}+{{k}_{2}}} \right)}\]
Correct Answer: D
Solution :
Given spring system has parallel combination, so \[{{k}_{eq}}={{k}_{1}}+{{k}_{2}}\] and time period \[T=2\pi \sqrt{\frac{m}{({{k}_{1}}+{{k}_{2}})}}\]
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