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Q.

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1kg, the angular frequency is $ω_{1} .$ When the mass block is 2 kg the angular frequency is $ω_{2} .$ The ratio $\frac{ω_{2}}{ω_{1}}$ is

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a

2

b

1/ $\sqrt{2}$

c

1/2

d

$\sqrt{2}$

answer is C.

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Detailed Solution

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$ω = \sqrt{\frac{k}{m}} . so, ω \propto \frac{1}{\sqrt{m}}$

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

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