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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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