Question 284: Oscillations

Question

A mass ' $m$ ' attached to a spring oscillates with a period of 3 second. If the mass is increased by 0.6 kg , the period increases by 3 second. The initial mass ' $m$ ' is equal to

Accepted Answer

$$\begin{array}{ll} 
& 	ext { Time period, } \
& \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}} \quad	ext{.... (i)}\
	herefore \quad & \mathrm{~T}_1=2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}} \quad	ext{.... [From (i)]}\
	herefore \quad & 3=2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}} \quad	ext { .....(given, } \mathrm{T}_1=3 \mathrm{~s} 	ext { ) }\
& \frac{9}{4 \pi^2}=\frac{\mathrm{m}}{\mathrm{k}} \
	herefore \quad & \mathrm{k}=\frac{4 \pi^2 \mathrm{~m}}{9}\quad	ext{.... (ii)}
\end{array}$$
$$\begin{aligned}
&	ext { When mass is increased by } 0.6 \mathrm{~kg}\
&\begin{aligned}
& T_2=2 \pi \sqrt{\frac{m+0.6}{k}} \quad	ext{... [From (i)]}\
& \left.\left.6=\sqrt{\frac{m+0.6}{k}} \quad \ldots 	ext { [given } T_2=3+3=6 \mathrm{~s}ight)ight] \
& \frac{36}{4 \pi^2}=\frac{m+0.6}{k} \
& \frac{36}{4 \pi^2}=(m+0.6) \frac{9}{4 \pi^2 m} \
& 4 m=m+0.6 \
& m=0.2 k g
\end{aligned}
\end{aligned}$$

Answer

0.1 kg

Answer

0.2 kg

Answer

0.3 kg

Answer

0.4 kg

Oscillations

A mass ' m ' attached to a spring oscillates with a period of 3 second. If the mass is increased by 0.6 kg , the period increases by 3 second. The initial mass ' m ' is equal to

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