JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Spring Pendulum

  • question_answer
    A mass m is vertically suspended from a spring of negligible mass; the system oscillates with a frequency n. What will be the frequency of the system if a mass 4 m is suspended from the same spring                                             [CBSE PMT 1998]

    A)            \[n/4\]                                    

    B)            \[4n\]

    C)            \[n/2\]                                    

    D)            \[2n\]

    Correct Answer: C

    Solution :

                       \[n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}\Rightarrow n\propto \frac{1}{\sqrt{m}}\Rightarrow \frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}\]            \[\Rightarrow \frac{n}{{{n}_{2}}}=\sqrt{\frac{4m}{m}}\Rightarrow {{n}_{2}}=\frac{n}{2}\]


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