Explanation of a Foucault pendulum

The equations of motion of a Foucault pendulum is given by:

$$\ddot{x} = 2\omega \sin\lambda \dot{y} - \frac{g}{L}x$$ $$\ddot{y} = -2\omega \sin\lambda \dot{x} - \frac{g}{L}y$$

where $\omega$ is the rotational frequency of the earth which has a value of $7.27 x 10^-5$, $\lambda$ is the latitude of where the pendulum is, $g$ is the acceleration due to gravity, $L$ is the length of the pendulum's string. What I don't know is what does $x$ and $y$ represent? I have read some derivations of these equations but I really cant figure out what they are trying to say.

1 Answer

The $x$ represents the x-coordinate of the pendulum.

The $y$ represents the y-coordinate of the pendulum.

$x$ and $y$ are perpindicular to each other, but parallel to the Earth's surface. $z$, not mentioned in these equations is height.

• So it represents the position of the bob? – user61835 Mar 9 '13 at 5:40
• Yes, that's right. – Kenshin Mar 9 '13 at 5:43
• Might as well ask this, do you have any idea how to simulate a foucault pendulum in matlab? – user61835 Mar 9 '13 at 5:45
• @user61835 mathworks.com.au/help/simulink/examples/… <- explains how to model it in matlab. – Kenshin Mar 9 '13 at 5:59