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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)
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