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- Thread starter dwsmith
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Is the period I obtained correct? Is that the yes or is the yes it is the reciprocal?Yes:

$\displaystyle f=\frac{1}{\tau}$

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- Jan 26, 2012

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If you have a function $\sin(kt)$, find the period $\tau$ by setting $k\tau=2\pi$.

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I agree with the period you found and with the relationship between frequency and period that you stated.

$\displaystyle \tau=\frac{2\pi}{\omega}$

In your case $\displaystyle \omega=\frac{\pi e}{L}\left(n+\frac{1}{2} \right)$

And so:

$\displaystyle \tau=\frac{2\pi}{ \frac{\pi e}{L} \left(n+ \frac{1}{2} \right)}= \frac{2L}{e\left(n+\frac{1}{2} \right)}$

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If you have a function $\sin(kt)$, find the period $\tau$ by setting $k\tau=2\pi$.

Is there a difference between frequency and natural frequency (eigenfrequencies)?

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- Jan 26, 2012

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The term "natural frequency" refers to resonance. So if you have a forced mass-spring system, e.g., and you tune the forcing function to the same frequency as a term in the homogeneous solution, you end up with unstable behavior.Is there a difference between frequency and natural frequency (eigenfrequencies)?

The term "frequency" just refers to what's going on in this thread.

There's also the term "angular frequency", which is represented by $\omega=2\pi f$.

Hope that's as clear as mud.

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I am trying to find the natural frequency (eigenfrequency) of $u$.The term "natural frequency" refers to resonance. So if you have a forced mass-spring system, e.g., and you tune the forcing function to the same frequency as a term in the homogeneous solution, you end up with unstable behavior.

The term "frequency" just refers to what's going on in this thread.

There's also the term "angular frequency", which is represented by $\omega=2\pi f$.

Hope that's as clear as mud.

How would I do that then?

$$

u(x,t) = \sum_{n = 1}^{\infty}\sin\left[\frac{\pi x}{L}\left(n + \frac{1}{2}\right)\right]\left\{A_n\cos\left[\frac{\pi ct}{L}\left(n + \frac{1}{2}\right)\right] + B_n\sin\left[\frac{\pi ct}{L}\left(n + \frac{1}{2}\right)\right]\right\}

$$

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- #9

- Jan 26, 2012

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Well, I could be wrong, but I would say that all of yourI am trying to find the natural frequency (eigenfrequency) of $u$.

How would I do that then?

$$

u(x,t) = \sum_{n = 1}^{\infty}\sin\left[\frac{\pi x}{L}\left(n + \frac{1}{2}\right)\right]\left\{A_n\cos\left[\frac{\pi ct}{L}\left(n + \frac{1}{2}\right)\right] + B_n\sin\left[\frac{\pi ct}{L}\left(n + \frac{1}{2}\right)\right]\right\}

$$

$$f_{n}=\frac{c\left(n + \frac{1}{2}\right)}{2L}$$

are the eigenfrequenc