A mass m attached to a spring oscillates with a period of 3,s . If mass is increased by 1,kg period

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13.Oscillations

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A mass $m$ attached to a spring oscillates with a period of $3\,s$. If the mass is increased by $1\,kg$ the period increases by $1\,s$. The initial mass $m$ is

A

$\frac{7}{9}\,kg$

B

$\frac{9}{7}\,kg$

C

$\frac{14}{7}\,kg$

D

$\frac{18}{7}\,kg$

Solution

$\frac{\mathrm{T}_{1}}{\mathrm{T}_{2}}=\sqrt{\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}}$

$\Rightarrow \frac{\mathrm{T}}{\mathrm{T}+1}=\sqrt{\frac{\mathrm{M}}{\mathrm{M}+1}}$

$\Rightarrow \frac{3}{4}=\sqrt{\frac{M}{M+1}}$

$\Rightarrow \frac{9}{16}=\frac{\mathrm{M}}{\mathrm{M}+1} \Rightarrow 9 \mathrm{M}+9=16 \mathrm{M}$

$\Rightarrow 7 \mathrm{M}=9 \Rightarrow \mathrm{M}=\frac{9}{7} \mathrm{Kg}$

Standard 11

Physics

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