Question

Problem 2. A massless string of length L passes through horizontal table. A hole in a a end of the string mo ves frictionlessly point pass M at one on the table (i.e. with two degrees of freedom), and another point mass m hangs vertically from the other end. The system is in a uniform gravitational field with acceleration g. M m (a) Write the Lagrangian for the system. [13 points (b) Suppose the mass M on the table initially has a speed . Under what conditions will the hanging mass remain stationary? 13 points (c) Starting from the situation in part (b), the hanging mass is pulled down very slightly and then released. Compute the angular frequency of the subsequent oscillatory motion of the hanging mass. 14 points]

Answer 1

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