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40 points. A train is moving along a straight line in a prescribed way: in other words, the coordinate \(X(t)\) of the train at the time t is given. A train car is carrying a cart with a pendulum. The cart without the pendulum has the mass M and can move along the car without friction. The cart is attached to the train car with a spring of stiffness c and equilibrium length l. There is a pendulum on the cart with a bob of mass m that can swing freely and without friction. All the mass of the pendulum is concentrated in the bob; the rest of the pendulum is massless. The length of the pendulum is l and is constant.

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Sample Midterm and Final Exams

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  • 发表日期：

    2025年

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  • Vakhtang Putkaradze

摘要

40 points. A train is moving along a straight line in a prescribed way: in other words, the coordinate \(X(t)\) of the train at the time t is given. A train car is carrying a cart with a pendulum. The cart without the pendulum has the mass M and can move along the car without friction. The cart is attached to the train car with a spring of stiffness c and equilibrium length l. There is a pendulum on the cart with a bob of mass m that can swing freely and without friction. All the mass of the pendulum is concentrated in the bob; the rest of the pendulum is massless. The length of the pendulum is l and is constant.