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BCECE Engineering BCECE Engineering Solved Paper-2009

  • question_answer
    A body executing linear simple harmonic motion has a velocity of \[3\,m{{s}^{-1}}\] when its displacement is 4 cm and a velocity of \[4\,m{{s}^{-1}}\] when its displacement is 3 cm. What is the amplitude of oscillation?

    A)  5 cm                                     

    B)  7.5 cm                 

    C)  10 cm                  

    D)         12.5 cm

    Correct Answer: A

    Solution :

    Velocity of SHM \[v=\omega \sqrt{{{a}^{2}}-{{y}^{2}}}\] \[\Rightarrow \]\[9={{\omega }^{2}}[{{a}^{2}}-16]\]                        ?(i) Similarly, \[16={{\omega }^{2}}[{{a}^{2}}-9]\]      ?(ii) Dividing Eq.(ii) by Eq. (i), we get \[\frac{16}{9}=\frac{[{{a}^{2}}-9]}{[{{a}^{2}}-16]}\]                 \[\Rightarrow \]               \[{{a}^{2}}=25\]                 or            \[a=\,5\,cm\]


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