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