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

@t=0 x=0 and x'=0

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?

[BA.]

Yeah, so, I slept at a Holiday Inn Express last night and whipped this up to try to help out....


There are 3 ways that I know of to solve this equation. 1) guess the right function, 2) Laplace transforms.....which is what the problem seems to call for, or 3) just solve the thing by choosing the homogenous and particular solutions and adding them, then substituting them back into the equation and use the boundary conditions to solve for the constants.

On a multiple choice test, they are looking for easy answers and most likely wouldn't break down into awkward numbers like 65.088. So my advice is to memorize simple Laplace transformations, the Laplace transformation rules for differentiation, and the technique of partial fraction decomposition. Using this combined with the correct equation should yield easily solvable roots.
The homogenous solution to his equation is something like x = Ae^[(1+8j)t] + Be^^[(1-8j)t]...give or take a negative sign. The complete solution is something like x = Ae^[(1+8j)t] + Be^^[(1-8j)t] +Csin(2t) +Dcos(2t).

[Slow Ride]

Yeah, so, I slept at a Holiday Inn Express last night and whipped this up to try to help out....


There are 3 ways that I know of to solve this equation. 1) guess the right function, 2) Laplace transforms.....which is what the problem seems to call for, or 3) just solve the thing by choosing the homogenous and particular solutions and adding them, then substituting them back into the equation and use the boundary conditions to solve for the constants.

On a multiple choice test, they are looking for easy answers and most likely wouldn't break down into awkward numbers like 65.088. So my advice is to memorize simple Laplace transformations, the Laplace transformation rules for differentiation, and the technique of partial fraction decomposition. Using this combined with the correct equation should yield easily solvable roots.
The homogenous solution to his equation is something like x = Ae^[(1+8j)t] + Be^^[(1-8j)t]...give or take a negative sign. The complete solution is something like x = Ae^[(1+8j)t] + Be^^[(1-8j)t] +Csin(2t) +Dcos(2t).

Thanks, the more I work on these types of problems the more I realize I'm going need to really dig into my Diff EQ. I'm going to dig out my old books and homework, maybe that will knock the rest of the cobwebs out of my head.

[MrQuick]

...im still trying to put out my smoldering TI-83plus.

[WS6]

I don't know La whatever transformers yet so I'd go at that with second derivative nonhomogenous right part rules. My answer wouldn't look like BA's though except for the Csin2t + Dcos2t part.

I hate Diff Eqs. It's probably my teacher though