- #1
logan3
- 83
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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-\frac{\pi}{2}it
2. Harmonic oscillator equation:
\frac{d^{2}y}{dt^{2}} = -ω^{2}y
frequency (f) = \frac{ω}{2\pi}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 \frac{\pi}{2} in the second. Plugging both of these into the frequency equations yields:
f = \frac{3}{2\pi} = 0.48 and
f = \frac{\frac{\pi}{2}}{2\pi} = 0.25
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-\frac{\pi}{2}it
2. Harmonic oscillator equation:
\frac{d^{2}y}{dt^{2}} = -ω^{2}y
frequency (f) = \frac{ω}{2\pi}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 \frac{\pi}{2} in the second. Plugging both of these into the frequency equations yields:
f = \frac{3}{2\pi} = 0.48 and
f = \frac{\frac{\pi}{2}}{2\pi} = 0.25
Thank-you.
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