A mass m = 8,kg is attahced to a spring as shown in figure and held in position so that spring remai

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13.Oscillations

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A mass $m = 8\,kg$ is attahced to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is $200\,N/m$. The mass $m$ is then released and begins to undergo small oscillations. The maximum velocity of the mass will be ..... $m/s$ $(g = 10\,m/s^2)$

A

$1$

B

$2$

C

$4$

D

$5$

Solution

$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{K}}}$

or $\omega=\sqrt{\frac{\mathrm{K}}{\mathrm{M}}}=5 \mathrm{rad} / \mathrm{sec}$

and $A=m g / K=2 / 5 \mathrm{m}$

$\mathrm{v}_{\max }=\omega \mathrm{A}=2 \mathrm{m} / \mathrm{s}$

Standard 11

Physics

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