Problem 3. Consider a solid rectangular prism with mass M uniformly distributed, and sides a, a,...

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Problem 3. Consider a solid rectangular prism with mass M uniformly distributed, and sides a, a, b, as shown. a a Suppose that the object is suspended in a uniform gravitational field g from one of its edges of length a, with that edge kept fixed and horizontal, and is free to swing as a pendulum. (a) [20 points] Find a Lagrangian (with one degree of freedom) describing the motion. (b) [10 points] Suppose that the pendulum starts from rest with its square side horizontal. Find the maximum speed reached by any part of the pendulum. (c) [10 points] Find the angular frequency of small oscillations. Problem 3. Consider a solid rectangular prism with mass M uniformly distributed, and sides a, a, b, as shown. a a Suppose that the object is suspended in a uniform gravitational field g from one of its edges of length a, with that edge kept fixed and horizontal, and is free to swing as a pendulum. (a) [20 points] Find a Lagrangian (with one degree of freedom) describing the motion. (b) [10 points] Suppose that the pendulum starts from rest with its square side horizontal. Find the maximum speed reached by any part of the pendulum. (c) [10 points] Find the angular frequency of small oscillations.