A block of mass $ m = 1 $ is sitting on a table and is attached to a spring of strength $ k = 5 $ so that it can slide horizontally on the table. The coefficient of linear friction between the block and the table is $ b = 2 $, and an external force of $ F(t) = 13 \cos(3t) $ acts on it. Find the general solution to this differential equation, and determine if the spring-mass system is over-damped, critically damped, or under-damped.

Given information: The mass of the block (m) = 1 kg The strength of the spring (k) = 5 The…

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