- #1

logan3

- 82

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These are practice problems, not homework. Just wanting to check to see if my process and solutions are correct.

f(x) = e

f(x) = e

[itex]\frac{d^{2}y}{dt^{2}} = -ω^{2}y[/itex]

frequency (

Thank-you.

**1.**Given the following functions as solutions to a harmonic oscillator equation, find the frequency*f*correct to two significant figures:f(x) = e

^{-3it}f(x) = e

^{-[itex]\frac{\pi}{2}[/itex]it}**2. Harmonic oscillator equation:**[itex]\frac{d^{2}y}{dt^{2}} = -ω^{2}y[/itex]

frequency (

*f*) = [itex]\frac{ω}{2\pi}[/itex]**3.**Since a solution to the harmonic oscillator equation can be in the form of e^{-iωt}, then ω = 3 in the first solution and [itex]\frac{\pi}{2}[/itex] in the second. Plugging both of these into the frequency equations yields:*f*= [itex]\frac{3}{2\pi} = 0.48[/itex] and*f*= [itex]\frac{\frac{\pi}{2}}{2\pi} = 0.25[/itex]Thank-you.

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