Solve Problem 13.30 for an undamped system with a soft spring: [ddot{x}+omega_{n}^{2}left(1-k^{2} x^{2} ight) x=0] Data From Problem 13.30:- Identify the singularity and investigate the

Solve Problem 13.30 for an undamped system with a soft spring:

\[\ddot{x}+\omega_{n}^{2}\left(1-k^{2} x^{2}\right) x=0\]

Data From Problem 13.30:-

Identify the singularity and investigate the nature of solution near the singularity for an undamped system with a hard spring:
\[\ddot{x}+\omega_{n}^{2}\left(1+k^{2} x^{2}\right) x=0\]