Math help(worth a try)

[Slow Ride]

As some of you may or may not know, I am taking the Professional Engineering exam at the end of this month. It's a real bitch trying to remember all of college 9 years after I graduated. My LaPlace Transforms are VERY rusty, which is one way to solve these problem, but time consuming. Also the PE is setup that you have an average of 6 minutes per problem so time is precious. Anyone out there have a faster way of solving this type of problem? I can not use a graphing calculator.

here is one of the functions I came up with for a sample problem.

x" + 2x' + 65.088x = 16 cos 2t

I got to this point in about 3.5 minutes after solving for the spring rate, natural frequency, damping factor, and max deflection of a forced and damped vibratory system. What methods do you guys have for solving for the response function in around 3 minutes?