Simple harmonic motion (doubt in the derivation of equation)

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The discussion centers on the derivation of the equation for simple harmonic motion, specifically the relationship F = -kx for a mass on a spring. It explains that by rearranging the equation to a = -(k/m)x, one can define ω² = k/m, leading to the form a = -ω²x. This definition is not arbitrary; it stems from the known solution to the differential equation ma = -kx, which results in a sinusoidal function. The angular frequency ω can be derived from this sinusoidal function by solving the differential equation. Understanding this connection clarifies the relationship between spring constant, mass, and angular frequency in simple harmonic motion.
kandyfloss
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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?
 
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kandyfloss said:
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).
 
I didn't get it.How do you find the angular frequency from the sinusoidal function of ma=-kx (or m d2x/dt2 = -kx ?
 
aah! great stuff,thanx.
 

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