# Hooke's Law and y=mx+c

1. Nov 21, 2012

### iamBevan

Hi guys - we did an experiment at college putting some weights on a spring for our Hooke's Law module. When I graph it I get a value for c, in the equation y=mx+c. Is this correct? Will c have a value?

Thanks.

2. Nov 21, 2012

### rock.freak667

Well Hooke's law says that F is proportional to x. So if you get a value for c, then it should be small.

3. Nov 21, 2012

### iamBevan

It is pretty small - I remember hearing that c would be the force required to hold the spring tight, wasn't sure if that was true or not...

4. Nov 21, 2012

### Mandelbroth

Hooke's Law states that $F_{spring} = -kx$, where k is the spring constant and x is the displacement vector.

Theoretically, you should get a value for c. However, this value is 0. If you are getting anything that deviates too greatly from 0, it is probably an error.

What method are you using to find the line? Are you using linear regression?

5. Nov 21, 2012

### iamBevan

y2-y1/x2-x1

6. Nov 21, 2012

### Mandelbroth

So...$\frac{Δy}{Δx}$? How many trials did you do? I would imagine that using $\frac{Δy}{Δx}$ with more than 2 points would get...weird.

Try making a least-squares regression line.

The equation will follow the model of $\hat{y} = a + bx$, where $b = r \cdot \frac{S_{y}}{S_{x}}$ and $a = \bar{y} - b\bar{x}$.

For help...
$S_{x} = \sqrt{\frac{1}{n-1}\sum{(x_{i} - \bar{x})}^{2}}$, where n is the number of trials you did and xi is the value of x for trial #i. Follow the same process for Sy, except replace the x's with y's.

$r = \frac{1}{n-1}\sum{(\frac{x_{i} - \bar{x}}{S_{x}})}(\frac{y_{i} - \bar{y}}{S_{y}})$.

Don't worry if this looks complicated. It really isn't. Additionally, you might get a better looking (and possibly more accurate) line.

Out of curiosity, how did you use $\frac{Δy}{Δx}$ to do this, if you did more than two trials?

7. Nov 21, 2012

### Staff: Mentor

In your experiment, what is the definition of x? Does x represent the amount that the length of the spring increases (relative to having no force on the spring), or is it the distance from some arbitrary spatial reference point to the end of the spring where the force is applied?

8. Nov 21, 2012

### rock.freak667

Your value for 'c' should be close to zero as this would represent errors in measurement and so on. So you will not have to figure what qualitatively 'c' represents.