Question

Use Laplace's method to solve

A mass of 1 slug is attached to a spring whose constant is 5 lb/ft. Initially, the mass is released 1 foot below the equilibrium position with a downward velocity of 3 ft/s, and the subsequent motion takes place in a medium that offers a damping force that is 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) = 8 cos 2t + 2 sin 2t

x(t) = ?

(b) Graph the transient and steady-state solutions on the same coordinate axes.

(c) Graph the equation of motion.

Answer 1

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(b) Trankiceut Sot + $4ady aatu hie tranfint aln ) -o Co 12 in oud lue S4ady-vtetu Aln in and

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c) Graph of the equation of motion in red.

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