engineering recuitment NMDC Junior Officer (Trainee) Mock Test 2024 Mechanical Vibrations Undamped Free Vibration
Consider a two degree of freedom system as shown in the figure, where PQ is a rigid uniform rod of length, b and mass m.
Assume that the spring deflects only horizontally and force F is applied horizontally at Q. For this system, the Lagrangian, L is
1
\( \frac{1}{2}\left( {M + m} \right){\dot x^2} + \frac{1}{2}mb\dot \theta \dot x\cos \theta + \frac{1}{6}m{b^2}{\dot \theta ^2} - \frac{1}{2}k{x^2} + mg\frac{b}{2}\cos \theta \)
2
\(\frac{1}{2}m{\dot x^2} + \frac{1}{2}mb\dot \theta \dot x\cos \theta + \frac{1}{6}m{b^2}{\dot \theta ^2} - \frac{1}{2}k{x^2} + mg\frac{b}{2}\cos \theta + fb\sin \theta \)
3
\(\frac{1}{2}m{\dot x^2} + \frac{1}{2}mb\dot \theta \dot x\cos \theta + \frac{1}{6}m{b^2}{\dot \theta ^2} - \frac{1}{2}k{x^2} \)
4
\( \frac{1}{2}\left( {M + m} \right){\dot x^2} + \frac{1}{2}mb^2\dot \theta^2 - \frac{1}{2}k{x^2} + mg\frac{b}{2}\cos \theta \)