AIIMS AIIMS Solved Paper-2014

  • 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) \[T=2\pi \sqrt{\frac{m}{8k}}\]

    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 \[{{k}_{1}}+{{k}_{2}}=2k\] \[{{k}_{3}}+{{k}_{4}}=4k\] \[\frac{1}{{{k}_{eq}}}=\frac{1}{2k}+\frac{1}{2k}\] \[{{k}_{eq}}=k\] \[T=2\pi \sqrt{\frac{m}{k}}\]


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