A mass weighing 16 pounds stretches a spring (8/3) feet. The mass is initially r

Question

A mass weighing 16 pounds stretches a spring (8/3) feet. The
mass is initially released from rest from a point 2 feet
below the equilibrium position, and the subsequent
motion takes place in a medium that offers a damping
force that is numerically equal to (1/2) the instantaneous
velocity. Find the equation of motion if the mass is
driven by an external force equal to f(t) =10 cos(3t).

Setting the problem up I get k = 6, x(0) = 2, x'(0)=0, and mass m = 1/2.

using mx" + Bx' + kx = f(t):

(1/2)x"+(1/2)x'+6x=10cos(3t). I've multiplied that by two to get:

x" + x' + 12x = 20cos(3t). Setting x" + x' + 12x = 0, I find roots of (-1+47i)/2 and (-1-47i)/2.

From there it starts to get really messy and I'm not sure how to procede. Please show all work and assume the "down" direction is positive and the "up" direction is negative if needed for velocities and/or position. Thanks!

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