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Physics
Classical Physics
Exploring the Origin of x=e^(rt) in Simple Harmonic Motion
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[QUOTE="Nugatory, post: 6061566, member: 382138"] Are you asking where ##x=e^{rt}## came from? It's an educated guess as to the form of the solution. You look at ##\frac{d^2x}{dx^2}+\frac{k}{m}x=0##, you see that this can only work if the second time derivative of ##x## is a multiple of ##x##, you remember that ##x=e^{rt}## has this property so you try substituting that into the equation and see if it works. Differential equations are solved this way so often that there's even a word for the initial educated guess as to the form of the solution: "ansatz". [/QUOTE]
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Physics
Classical Physics
Exploring the Origin of x=e^(rt) in Simple Harmonic Motion
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