For a simple harmonic motion in a mass–spring system shown, the surface is frictionless. When the mass of the block is 1 kg, the angular frequency is . When the mass of the block is 2 kg, the angular frequency is . The ratio is [2023]

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Solution

Q.
For a simple harmonic motion in a mass–spring system shown, the surface is frictionless. When the mass of the block is 1 kg, the angular frequency is $ω_{1}$ . When the mass of the block is 2 kg, the angular frequency is $ω_{2}$ . The ratio $ω_{2} / ω_{1}$ is [2023]

1 $\sqrt{2}$

2 $\frac{1}{\sqrt{2}}$

3 $2$

4 $\frac{1}{2}$

Ans.
(2)

$ω = \sqrt{\frac{k}{m}}$

$\frac{ω_{2}}{ω_{1}} = \sqrt{\frac{m_{1}}{m_{2}}} = \sqrt{\frac{1}{2}}$

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