A solid sphere of radius R carries a positive charge Q distributed uniformly throughout its volume. A very…

Electric field inside a uniformly charged solid sphere is given by, $E=\frac{Qr}{4\pi {\epsilon }_0{R}^3}$.

Therefore, the force on the negative charge $-q$ at distance $r$ from the centre will be $F=-\frac{Qrq}{4\pi {\epsilon }_0{R}^3}$.

Comparing it with $F=-kx$, $k=\frac{Qq}{4\pi {\epsilon }_0{R}^3}$.

Now the frequency of the oscillation is $f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}=\frac{1}{2\pi }\sqrt{\frac{Qq}{4\pi {\epsilon }_0{R}^{3}m}}$.