Question

Mass-String-Damper system:

The molecular bond due to intermolecular forces is flexible. A diatomic molecule like oxygen (O_2), if disturbed, will oscillate to and fro the equilibrium position ( minimum potential energy) approximated by the equation: mu d^2x/dt^2+kx=0 Where mu is the reduced mass of the system mu = m_02 / 2 and k is the spring constant. The mu for the Oxygen molecule (O_2) is 1.33 x 10^-26 kg and k =1195 N/m. What is the natural frequency of O_2 ? What will happen to the molecule if it is forced by an external source to vibrate with a frequency equal to its natural frequency? Explain in detail. Compare the above results with that of Hydrogen molecule ( H_2) u = 0.83 x 10 kg and k = 575 N/m, and Nitrogen molecule (N_2) mu = 1.16 x 10^-26 kg and k = 2300 N/m, Can one conclude that the natural frequency of heavier diatomic molecules is lower than that of the lighter molecules? Justify your answer.

Answer 1