A mass $m$ attached to a spring oscillates every $2\, sec$. If the mass is increased by $2 \,kg$, then time-period increases by $1\, sec$. The initial mass is ..... $kg$
AIIMS 2000, Medium
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$T = 2\pi \sqrt {\frac{m}{k}} $
$ \Rightarrow \frac{{{T_2}}}{{{T_1}}} = \sqrt {\frac{{{m_2}}}{{{m_1}}}} $
==> $\frac{3}{2} = \sqrt {\frac{{m + 2}}{m}} $
$ \Rightarrow \frac{9}{4} = \frac{{m + 2}}{m}$
$ \Rightarrow m = \frac{8}{5}kg = 1.6\;kg$
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