Answer
$100\;g$
Work Step by Step
Let $m$ be the mass of first object and $k$ is spring constant. Therefore the frequency of first object is given by
$f=\frac{1}{2\pi}\sqrt {\frac{k}{m}}$
After adding the mass of 300 g, the frequency becomes
$f^{'}=\frac{1}{2\pi}\sqrt {\frac{k}{m+300}}$
According to the given condition
$f^{'}=\frac{f}{2}$
or, $\frac{1}{2\pi}\sqrt {\frac{k}{m+300}}=\frac{1}{2}\times\frac{1}{2\pi}\sqrt {\frac{k}{m}}$
or, $\frac{k}{m+300}=\frac{1}{4}\times\frac{k}{m}$
or, $\frac{1}{m+300}=\frac{1}{4}\times\frac{1}{m}$
or,$ 4m=300+m$
or, $m=100\;g$
Therefore, the mass of the first object is $100\;g$
