7.23* A small cart (mass m) is mounted on rails inside a large cart. The two...

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7.23* A small cart (mass m) is mounted on rails inside a large cart. The two are attached by a spring (force constant k) in such a way that the small cart is in equilibrium at the midpoint of the large. The distance of the small cart from its equilibrium is denoted x and that of the large one from a fixed point on the ground is X, as shown in Figure 7.13. The large cart is now forced to oscillate such that X = A cos wt, with both A and a fixed. Set up the Lagrangian for the motion of the small cart and show that the Lagrange equation has the form 7.23* A small cart (mass m) is mounted on rails inside a large cart. The two are attached by a spring (force constant k) in such a way that the small cart is in equilibrium at the midpoint of the large. The distance of the small cart from its equilibrium is denoted x and that of the large one from a fixed point on the ground is X, as shown in Figure 7.13. The large cart is now forced to oscillate such that X = A cos wt, with both A and a fixed. Set up the Lagrangian for the motion of the small cart and show that the Lagrange equation has the form

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sof Let x position of a small y cast dative to the initi... View the full answer