When a mass m is attached to a spring it oscillates with period 4 ,s . When an additional mass of 2

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13.Oscillations

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When a mass $m$ is attached to a spring it oscillates with period $4 \,s$. When an additional mass of $2 \,kg$ is attached to a spring, time period increases by $1 \,s$. The value of $m$ is ........... $kg$

A

$3.5$

B

$8.2$

C

$4.7$

D

$2.6$

Solution

(b)

$\omega_1=\sqrt{\frac{k}{m}}$

$\omega_2=\sqrt{\frac{k}{m+2}}$

$\frac{\omega_1}{\omega_2}=\sqrt{\frac{m+2}{m}}$

Since $\omega=\frac{2 \pi}{T}$

$\frac{T_2}{T_1}=\sqrt{\frac{m+2}{m}}$

$\left(\frac{5}{4}\right)^2=\frac{m+2}{m}$

$\frac{25}{16}=\frac{m+2}{m}$

$25 \,m=16 \,m+32$

$9 \,m=32$

$m=3 \frac{5}{9} \,kg$

$m=3.5 \,kg$

Standard 11

Physics

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