GATE ME 2021 Set 1 — Question 40

MCQ+2 / -0.67HardLagrange's EquationDynamicsEngineering Mechanics

Engineering Mechanics → Dynamics → Lagrange's Equation

Last updated 5 September 2026

Question

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

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\frac{1}{2}(M+m)\dot{x}^2 + \frac{1}{6}mb^2\dot{\theta}^2 - \frac{1}{2}kx^2 + mg\frac{b}{2}\cos\theta

\frac{1}{2}(M+m)\dot{x}^2 + \frac{1}{2}mb\dot{\theta}\dot{x}\cos\theta + \frac{1}{6}mb^2\dot{\theta}^2 - \frac{1}{2}kx^2 + mg\frac{b}{2}\cos\theta

\frac{1}{2}M\dot{x}^2 + \frac{1}{2}mb\dot{\theta}\dot{x}\cos\theta + \frac{1}{6}mb^2\dot{\theta}^2 - \frac{1}{2}kx^2

\frac{1}{2}M\dot{x}^2 + \frac{1}{2}mb\dot{\theta}\dot{x}\cos\theta + \frac{1}{6}mb^2\dot{\theta}^2 - \frac{1}{2}kx^2 + mg\frac{b}{2}\cos\theta + Fb\sin\theta

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