A mass of 1 slug is attached to a spring whose constant is 5 Ib/ft. Initially the mass is released 1 ft below the equilibrium position with a downward velocity of 5 ft/s, and the subsequent motion takes place in a medium that offers a damping force numerically equal to 2 times the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 12 cos 2t + 3 sin 2t. (b) Graph the transient and steady-state solutions on the same coordinate axes. (c) Graph the equation of motion.

A mass of 1 slug is attached to a spring whose constant is 5 Ib/ft. Initially the mass is released 1 ft below the equilibrium position with a downward velocity of 5 ft/s, and the subsequent motion takes place in a medium that offers a damping force numerically equal to 2 times the instantaneous velocity. (a) Find the equation of motion if the mass is driven by an external force equal to f(t) = 12 cos 2t + 3 sin 2t. (b) Graph the transient and steady-state solutions on the same coordinate axes. (c) Graph the equation of motion.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.19P

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