Three particles of mass m each situated at x1(t), x2(t) and x3(t) res…

Engineering Physics · Q60

Classical Mechanics

Engineering and GATE · Engineering Physics · question 60

Q60

Three particles of mass m each situated at x₁(t), x₂(t) and x₃(t) respectively are connected by two spring constants k and unstretched lengths

l

. The system is free to oscillate only in one-dimension along the straight line joining all the three particles. The Lagrangian of the system is

L = \frac{m}{2} [(\frac{d x _{1}}{d t})^{2} + (\frac{d x _{2}}{d t})^{2} + (\frac{d x _{3}}{d t})^{2}] - \frac{k}{2} (x_{1} - x_{2} - l)^{2} + \frac{k}{2} (x_{3} - x_{2} - l)

Answer

L = \frac{m}{2} [(\frac{d x _{1}}{d t})^{2} + (\frac{d x _{2}}{d t})^{2} + (\frac{d x _{3}}{d t})^{2}] - \frac{k}{2} (x_{1} - x_{3} - l)^{2} + \frac{k}{2} (x_{3} - x_{2} - l)

L = \frac{m}{2} [(\frac{d x _{1}}{d t})^{2} + (\frac{d x _{2}}{d t})^{2} + (\frac{d x _{3}}{d t})^{2}] - \frac{k}{2} (x_{1} - x_{2} - l)^{2} - \frac{k}{2} (x_{3} - x_{2} + l)^{2}

L = \frac{m}{2} [(\frac{d x _{1}}{d t})^{2} + (\frac{d x _{2}}{d t})^{2} + (\frac{d x _{3}}{d t})^{2}] - \frac{k}{2} (x_{1} - x_{2} - L)^{2} - \frac{k}{2} (x_{3} - x_{2} - l)^{2}

Answer: Option A

Answer: Option A

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Three particles of mass m each situated at x1(t), x2(t) and x3(t) respectively are connected by two spring constants k and unstretched lengths l . The system is free to oscillate only in one-dimension along the straight line joining all the three particles. The Lagrangian of the system is