How Do You Calculate the Wavelength of Particle Motion in Parametric Equations?

[Logarythmic]

I have two parametric equations for the speed of a particle in a plane:

$$\dot{x}(t) = A \left( 1 - cos{\Omega t} \right)$$
$$\dot{y}(t) = A sin{\Omega t}$$

The period is equal to $\Omega$. How do I find the wavelength of the motion?


The wavelength is just $\lambda = \Omega v$, where $v = \sqrt{\dot{x}^2 + \dot{y}^2}$ is the speed, right? But then the wavelength is not time invariant. Could my answer

$$\lambda = \Omega A \left( 2 - 2cos{\Omega t} \right)^{1/2}$$

really be correct?

 

[rl.bhat]

Here omega is not the period, but the angular velocity = 2pi/T where T is the period.

 

[Logarythmic]

I thought about that too, but it's stated in the problem that the motion is periodic with period $\Omega$. Anyway, my question still remains.

 

[Astronuc]

I thought about that too, but it's stated in the problem that the motion is periodic with period $\Omega$. Anyway, my question still remains.

Is this problem in a textbook, or was it given by a professor or teacher?

$\Omega$ as a period would seem to be incorrect since normally the arguments of sine and cosine are dimensionless, which is consistent with rl.bhat's comment.