Question

The Harmonic Oscillator frequency For Oxygen nucleus is approximately how much times of Harmonic Oscillatory frequency for Barium nucleus?

Answer 1

It is hard to tell without numerical values, but you can use the following expression to estimate is:

$$\frac{\omega_\text{O}}{\omega_\text{B}}=\sqrt{\frac{k_\text{O}m_{R\text{B}}}{k_{\text{B}}m_{R\text{O}}}},$$

where $k$ and $m_R$ are bond force constants and reduced masses for oxygen or barium.