MY QUICK GUIDE TO MECHANICS
1) EVERY QUESTION BASICALLY INVOLVES THE SOLVING OF TWO EQUATIONS
a) the vertical forces
b) the horizontal forces
Note that many forces aren't either horizontal or vertical. For these, we need to use our good friend TRIG.
If you get stuck, just draw a triangle. This is basic year 9 shit here people.
Now you have those equations, you're SET. Generally, the questions will require you to derive (no, nothing to do with calculus, please pay attention) some sort of relationship between forces from the vertical forces equation (this is the less complex one, nothing to do with imaginary numbers) and then use that to find a value of omega in the horizontal forces equation. omega is that thing that you think is a w.
Now, SOME QUESTIONS ARE DECEPTIVELY EASY. You go through the above steps and you say, Rorix, what the fuck? I didn't even need to use the vertical forces equation. Well, good on ya champ. For future reference, generally when they give you numbers, like r=20, you might not need to use both. Just use your brain, I'm not doing the test for you.
Now, THE LAST TRICK. SOMETIMES, JUST SOMETIMES, they'll tell you that the string length is l so your mrw^2 doesn't have an l. THIS IS REAL EASY TO FIX. LOOK AT YOUR DIAGRAM (did I mention a diagram was important? Draw a fucking diagram) and use your good friends SIN or COS (usually sin, unless you're using some nonorthodox angle).
LASTLY, WRITE SOME FUCKING UNITS DOWN. DO YOU WANT TO THROW MARKS OUT THE WINDOW OR DO YOU JUST NOT CARE?