- #1
Logarythmic
- 281
- 0
I have two parametric equations for the speed of a particle in a plane:
[tex]\dot{x}(t) = A \left( 1 - cos{\Omega t} \right)[/tex]
[tex]\dot{y}(t) = A sin{\Omega t}[/tex]
The period is equal to [itex]\Omega[/itex]. How do I find the wavelength of the motion?
The wavelength is just [itex] \lambda = \Omega v [/itex], where [itex]v = \sqrt{\dot{x}^2 + \dot{y}^2}[/itex] is the speed, right? But then the wavelength is not time invariant. Could my answer
[tex]\lambda = \Omega A \left( 2 - 2cos{\Omega t} \right)^{1/2}[/tex]
really be correct?
[tex]\dot{x}(t) = A \left( 1 - cos{\Omega t} \right)[/tex]
[tex]\dot{y}(t) = A sin{\Omega t}[/tex]
The period is equal to [itex]\Omega[/itex]. How do I find the wavelength of the motion?
The wavelength is just [itex] \lambda = \Omega v [/itex], where [itex]v = \sqrt{\dot{x}^2 + \dot{y}^2}[/itex] is the speed, right? But then the wavelength is not time invariant. Could my answer
[tex]\lambda = \Omega A \left( 2 - 2cos{\Omega t} \right)^{1/2}[/tex]
really be correct?