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As per given figures, two springs of spring constants \mathrm{ k} and \mathrm{ 2 k} are connected to mass \mathrm{ m}. If the period of oscillation in figure (a) is \mathrm{ 3 \mathrm{~s}, } then the period of oscillation in figure (b) will be \mathrm{ \sqrt{x} s. } The value of \mathrm{x} is ________.

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

      

\mathrm{K_{e q}=\frac{k(2 k)}{k+2 k} }

\mathrm{ K_{e q}=k_1+k_2 }

         \mathrm{=3K}

\mathrm{K_{e q}=\frac{2 k}{3} }

\mathrm{T_1=2 \pi \sqrt{\frac{m}{(2 k / 3)}}=1 }

\mathrm{T_2=2 \pi \sqrt{\frac{m}{3 k}} }

\mathrm{\frac{T_1}{T_2}=\frac{3^2}{T_2^2}=\frac{1 / (2 k / 3)}{1 / 3 k} }

\mathrm{\frac{9}{T_2^2}=\frac{3 \times 3}{2}=\frac{9}{2} }

\mathrm{T_2=\sqrt{2 s} }

\mathrm{x=2}

Posted by

Ramraj Saini

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