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A cart of mass M is placed on rails and attached to a wall with the help of a massless spring with constant k (as shown in the Figure below); the spring is in its equilibrium state when the cart is at a distance x0 from the wall. A pendulum of mass m and length ` is attached to the cart (as shown). (a) Write the Lagrangian L(x, x? , , ?) for the cart-pendulum system, where x denotes the position of the cart (as measured from a suitable origin) and  denotes the angular position of the pendulum. (b) From your Lagrangian, write the Euler-Lagrange equations for the generalized coordinates x and theeta in questin a L(X, x?,THEETA ,THEETA DASH)


A cart of mass M is placed on rails and attached to a wall with the help of a massless


spring with constant k (as shown in the Figure below); the spring is in its equilibrium state


when the cart is at a distance x0 from the wall. A pendulum of mass m and length ` is


attached to the cart (as shown).


(a) Write the Lagrangian L(x, x? , , ?) for the cart-pendulum system, where x denotes the


position of the cart (as measured from a suitable origin) and  denotes the angular position


of the pendulum.


(b) From your Lagrangian, write the Euler-Lagrange equations for the generalized coordinates


x and theeta                                                                                                                                                                in questin a L(X, x?,THEETA ,THEETA DASH)


Grade:12

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