Why is ω² defined as k/m in simple harmonic motion?

[kandyfloss]

F=-kx when talking about a mass at the end of a horizontal spring
therefore ma=-kx
rearranging we get a= -(k/m)x
then it says if we define ω²=k/m we then have a generic form :
a= -ω²x
My question is what does "if we define ω²=k/m" mean? where does this come from?is it just any random assumption?

 

[Doc Al]

My question is what does "if we define ω²=k/m" mean? where does this come from?is it just any random assumption?

They define it that way because they already know the answer. The solution to the differential equation ma=-kx (or m d²x/dt² = -kx) will be a sinusoidal function with an angular frequency given by ω = √(k/m).

 

[kandyfloss]

I didn't get it.How do you find the angular frequency from the sinusoidal function of ma=-kx (or m d²x/dt² = -kx ?

 

[Doc Al]

I didn't get it.How do you find the angular frequency from the sinusoidal function of ma=-kx (or m d²x/dt² = -kx ?

You have to solve the differential equation. See: http://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics_of_simple_harmonic_motion"

 

[kandyfloss]

aah! great stuff,thanx.