Simple harmonic motion (doubt in the derivation of equation)

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SUMMARY

The discussion centers on the derivation of the equation for simple harmonic motion, specifically the relationship F = -kx and its implications for acceleration. It establishes that the equation ma = -kx can be rearranged to a = -(k/m)x, leading to the definition of angular frequency as ω² = k/m. This definition is not arbitrary; it arises from the solution to the differential equation m d²x/dt² = -kx, which results in a sinusoidal function with angular frequency ω = √(k/m).

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  • Understanding of Newton's second law (F = ma)
  • Familiarity with differential equations
  • Knowledge of sinusoidal functions
  • Basic concepts of angular frequency
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  • Study the derivation of the differential equation for simple harmonic motion
  • Learn how to solve second-order differential equations
  • Explore the relationship between force, mass, and acceleration in oscillatory systems
  • Investigate the properties of sinusoidal functions in physics
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Students of physics, mechanical engineers, and anyone interested in understanding the principles of simple harmonic motion and its mathematical foundations.

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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