Two springs of force constant K and 2K are connected to a mass as shown below. frequency of oscillat

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13.Oscillations

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Two springs of force constant $K$ and $2K$ are connected to a mass as shown below. The frequency of oscillation of the mass is

A

$\frac{{3K}}{M}$

B

$\pi \,\sqrt {\frac{{6M}}{K}} $

C

$\frac{1}{{2\pi }}\,\sqrt {\frac{{3K}}{M}} $

D

$\frac{1}{\pi }\,\sqrt {\frac{K}{{6M}}} $

Solution

$\frac{1}{\mathrm{K}_{\mathrm{eq}}}=\frac{1}{\mathrm{K}_{1}}+\frac{1}{\mathrm{K}_{2}}$

$=\frac{1}{\mathrm{K}}+\frac{1}{2 \mathrm{K}}$

$\mathrm{Keq}=\frac{2 \mathrm{K}}{3}$

$\mathrm{n}=\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{K} / 3}{\mathrm{M}}}=\frac{1}{\pi} \sqrt{\frac{\mathrm{K}}{6 \mathrm{M}}}$

Standard 11

Physics

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