question_answer

 As shown in figure, a simple harmonic motion oscillator having identical four springs has time period

A) \[T=2\pi \sqrt{\frac{m}{4k}}\]                   

B) \[T=2\pi \sqrt{\frac{m}{2k}}\]

C) \[T=2\pi \sqrt{\frac{m}{k}}\]                      

D) \[T=2\pi \sqrt{\frac{2m}{k}}\]

Correct Answer: C

Solution :

                \[{{k}_{1}}\] and \[{{k}_{2}}\] are parallel and \[{{k}_{3}}\] and \[{{k}_{4}}\] are parallel. The two combinations are in series with each other. \[\therefore \]  \[{{k}_{1}}+{{k}_{2}}=k+k=2k\] \[{{k}_{3}}+{{k}_{4}}=k+k=2k\] \[\frac{1}{{{k}_{eq}}}=\frac{1}{2k}+\frac{1}{2k}\] \[\Rightarrow \]               \[{{k}_{eq}}=k\] Time period \[T=2\pi \sqrt{\frac{m}{k}}\]