Consider a system of two identical pendula of mass m, each suspended on a massless spring whose spring constant is k. The length of each spring at equilibrium is . The two pendula are coupled by a spring with spring constant ' and equilibrium length L. The generalised coordinates (21,01} and {22,02} encode the displacements of the two pendula from their equilibrium positions. Gravity acts downwards in the vertical direction. Here's a picture of the set up. L 01 ци Z1 k' e 02 k 22 L+AL (a) Consider for now the case of k' = 0, i.e., no coupling between the two pendula. Write down: (i) The kinetic energy, and (ii) The potential energy for pendulum 1 in this system in terms of the generalised coordinates {01, 1} and the physical properties of the system {m, l, k, g}. [Hint 1: There are two forms of potential energy in this reduced system. Hint 2: In polar coordinates, ||2 + |y2||² + 21012./

Consider a system of two identical pendula of mass m, each suspended on a massless spring whose spring constant is k. The length of each spring at equilibrium is . The two pendula are coupled by a spring with spring constant ' and equilibrium length L. The generalised coordinates (21,01} and {22,02} encode the displacements of the two pendula from their equilibrium positions. Gravity acts downwards in the vertical direction. Here's a picture of the set up. L 01 ци Z1 k' e 02 k 22 L+AL (a) Consider for now the case of k' = 0, i.e., no coupling between the two pendula. Write down: (i) The kinetic energy, and (ii) The potential energy for pendulum 1 in this system in terms of the generalised coordinates {01, 1} and the physical properties of the system {m, l, k, g}. [Hint 1: There are two forms of potential energy in this reduced system. Hint 2: In polar coordinates, ||2 + |y2||² + 21012./

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter15: Oscillations

Section: Chapter Questions

Problem 15.1CYU: Check Your Understanding Why would it hurt more if you snapped your hand with a ruler than with a...

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