Yo-yoing over the harmonic oscillator

AI Thread Summary
The discussion centers on understanding how the cosine function appears in the solution to the harmonic oscillator equation, d²x/dt² = -kx/m. The user seeks clarification on the relationship between the second derivative of the cosine function and the equation's structure. It is noted that the second derivative of -cos(θ) equals cos(θ), which aligns with the harmonic oscillator's characteristics. Additionally, the suggestion to explore the form x = a*cos(bt) is presented as a potential solution fitting the equation. Overall, the conversation emphasizes the mathematical foundations of harmonic motion and the role of trigonometric functions in its solutions.
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I've been looking around and trying to figure it out, but I can't seem to figure out how the cosine function get's into the solution to the HO equation d2x/dt2=-kx/m. I know this is extremely basic, but could someone indulge me?
 
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It is not so difficult to use a better notation!

Try to see whether x = acos(bt), where a and b are constants, fits with the equation

\frac{d^{2}x}{dt^{2}} = -(positive constant)x.
 
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