WyzAnt asked me to write a summary of pendulums for their self help section. It includes frequencies, amplitudes, and periods of pendulums, conservation of energy, forces on a pendulum, and motion of objects experiencing Simple Harmonic Motion. It can be found here:
http://www.wyzant.com/help/science/physics/pendulums
Most systems do not even reach their equilibrium conditions let alone...
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If you let processes that can go both forwards and backwards sit long enough, they will reach “dynamic equilibrium.” This sounds like an oxymoron because things at equilibrium are constant, right? Well, molecules are always spontaneously bumping into each other and exchanging energy. What we perceive as stuff moving in one direction just means that the rate of stuff in that direction is greater...
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You know by the Pythagorean theorem that a2 +b2 = c2 where a and b are the legs of the triangle and c is the hypotenuse or longest side. When they say the other two legs are consecutive integers, that means that x = x+1 or in this case c = b+1. By substituting c = b+1 and 7cm into...

This is a classic two equations with two unknowns type problem. The goal in the first step is to eliminate one of the variables by making an equivalent statement in terms of one variable. In order to get rid of one of the variables, substitute either
y = 2-x or ...

By the order of operations, multiplication comes before addition. The (x-2y+6z) is being mulitplied by -1, so distribute that through first. Then remember that addition is commutative and you can add/subtract like terms together, for example 3y + 4y = 7y.