Question

(25 points) anchored to two facing walls as shown in the figure. Inside the cart, a pendulum of mass m (not included in the mass M of the cart) and length l is hung from the ceiling, z is the displacement of the cart from its equilibrium position, and ф is the angle the pendulum makes with the vertical. 4. Coupled oscillators. A cart of mass M when empty is attached to two springs (a) Write down the kinetic and potential energies for the system in terms of z and Indicate which term or terms is responsible for the coupling between the oscillators (springs and pendulum). Then show that if a small angle approximation is applied the Lagrangian takes on a quadratic form. Specifically, when taking r and s lp as generalized coordinates, the M and K matrices, as defined in the formula section, are: 2k 0 M=(m+M m

Answer 1

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