# Power series question involving classical mechanics

1. May 4, 2010

### seboastien

1. The problem statement, all variables and given/known data
A heavy weight is suspended by a cable and pulled to one side by a force F. How much force is required to hold the weight in equilibrium at a given distance x to one side.
From classical mechanics, TcosX= W and TsinX=F. Find F/W as a power series of X(angle).

Often in a problem like this, what we know is not X, but x(displacement) and l(length of string).

Find F/W as a series of powers in x/l

2. Relevant equations

TcosX=W
TsinX=F

3. The attempt at a solution

How do I calculate the power series for tanX? I've searched online but the people at yahoo answers got it wrong
http://en.wikipedia.org/wiki/Taylor_series
Wikipedia gives the answer but no route to it.

SinX= x/l

cosX= ((l-x)(l+x))^0.5/l

F/W = x/(l-x)(l+x)^0.5??????

2. May 4, 2010

### vela

Staff Emeritus
You want things in terms of x/l. The sine already is, but the cosine isn't. Rewrite it slightly, like this

$$\cos X = \frac{\sqrt{l^2-x^2}}{l}} = \sqrt{1-\left(\frac{x}{l}\right)^2}$$

and go from there.