logan3
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These are practice problems, not homework. Just wanting to check to see if my process and solutions are correct.
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.
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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