Find frequency of mass in the setup shown below, when displaced from its equilibrium position.

\sqrt{\frac{3 k}{m}}

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\sqrt{\frac{k}{m}}

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\sqrt{\frac{2 k}{m}}

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\sqrt{\frac{m}{3 k}}

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Solution

The correct option is A $\sqrt{\frac{3 k}{m}}$
For a spring mass system, frequency of oscillation is
$f = \frac{1}{2 π} \sqrt{\frac{k_{e}}{m}} f \propto \sqrt{\frac{k_{e}}{m}}$
As given in figure springs are in parallel, here value of $k_{e}$ will become $2 k + k = 3 k$
$∴ f \propto \sqrt{\frac{3 k}{m}}$

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Find frequency of mass in the setup shown below, when displaced from its equilibrium position.

The correct option is A √3kmFor a spring mass system, frequency of oscillation is f=12π√kemf∝√kem As given in figure springs are in parallel, here value of ke will become 2k+k=3k ∴f∝√3km