I am trying to compute the Fourier transform of a square pulse with MATLAB's FFT.
Code:
Fs=1000; %Sampling rate (Hz)
T=1/Fs; %Sampling time interval
P=10; %Period of pulse
t=0:1/Fs:P/2; %Time axis
N=length(t);
x=rectpuls(t,P); %Pulse amplitude
n=pow2(nextpow2(N)); %Number of frequency...
Homework Statement
How to find for a Poisson distribution the number of successes for a given probability and mean. For example, for mean, \lambda, of 1, and a required probability of 0.01, what would the number of successes in the time interval be?Homework Equations...
Right, thanks.
If v = w^{3/2}, where w = \frac{2}{\mu_0}\left(\frac{dp}{dz}\frac{e^{3x}}{3}-C_1) , then with chain rule
\frac{dv}{dx} = \frac{w^{1/2}e^{3x}}{\mu_{o}}\frac{dp}{dz}
Hence
\int\frac{dv}{dx}dx = w^{3/2} + C_{2}\rightarrow \int w^{1/2}dx =...
I've ended up with:
u^{2}\mu_{o} = \frac{dp}{dz} \frac{x^{3}}{6}e^{3x} + C_{1}\frac{x^{2}}{2}e^{3x} + C_{2}xe^{3x} + C_{3}
Is that right? Can I say that e3x=r3? Though I don't believe this is the way its meant to be done as it is unsolvable with three constants. Thanks a lot for your help.
I see what I did wrong; I canceled both of the dr's when I integrated.
\frac{dp}{dz}=\mu_{o} \frac{du}{de^{x}} \frac{1}{e^{x}} \frac{d}{de^{x}}(e^{x} \frac{du}{de^{x}})
How would you go about rearranging it now into a function of u? Don't need to show latex, just need a hint. Thanks.
Homework Statement
\frac{dp}{dz}=\mu_{o}\frac{du}{dr}\frac{1}{r}\frac{d}{dr}(r \frac{du}{dr})
Homework Equations
The Attempt at a Solution
Multiply by r, and then integrate with respect to r to get:
\frac{dp}{dz}\frac{r^{2}}{2}+C_{1}=\mu_{o}ur \frac{du}{dr}
Divide by r and...
I did actually try that way also, with answer:
\frac{F_{1}}{F_{2}}=\frac{F_{2}\pm\sqrt{1+F_{2}^2}}{-F_{1}\pm\sqrt{1+F_{1}^2}}
I can't see how to simplify that either. But since F1 and F2 are constants, isn't it meaningless to take their roots?
Thanks
Homework Statement
Part of a larger problem. I know that
F_{1}^2+2F_{1}F_{2}-F_{2}^2=0
where F_{1} and F_{2} are x and y components of a force. Hence
\frac{F_{1}}{F_{2}}=1\pm\sqrt{2}
I can't see how that step is done.
Homework Equations
The Attempt at a Solution...