Recent content by Hechima

One way of thinking about this is that the Fourier Transform is a certain special case of the Laplace Transform, namely by a few assumptions and the substitution s=jω. Time-frequency is something that can be measured, and we have a certain intuition about it because of our senses- we can hear...

There is such a notion as a minimal phase reconstruction in signal processing. Here's an outline of the process: Suppose you have an analytic signal: x(t)=A(t)eiφ(t) Then (a) log of the signal would be: log(x(t)) = log(|A(t)|)+iφ(t) Now, what if we just have A(t)? You can take log(|A(t)|) and...

http://en.wikipedia.org/wiki/Terminal_velocity The drag force increases with velocity, and if the object is accelerating (e.g under gravity) the velocity is increasing with time. So, after some time the acceleration due to the drag force comes to oppose the acceleration due to gravity; the...

Try plotting your pull force versus linear dimension and see what you get. How about pull force versus cross sectional area?

I would recommend trying out your re-scaling using a simulator. Search for 'vizimag', it's free and relatively easy to use. It will also calculate magnetic forces, which is not a simple problem.

This can't be right, the integrand is a vector, and the result you state is a scalar. The integral is like a vector sum- what do you get when you add up all the tangent vectors to a circle going around the loop? (think about the vector sum around a polygon)

How did you arrive at your formula for the instantaneous frequency? I suspect that it might be off. If I calculate the instantaneous frequency using a different approach, with the analytical signal 'y' using your code: dy = diff(y)/0.01; dy(501) = 0; instfrq = imag(dy./y); I get...

In addition to choosing a state variable for each element that stores energy (the two capacitors and the one inductor), you should also consider that your state space model may look something like this: State: X1, X2, X3 \frac{d}{dt}X_{1}=aX_{1}+bX_{2}+cX_{3}...

Here's one way of looking at it that I believe is useful: Consider the function f(t) = A cos(\omega_0t) = Real\{A e^{i \omega_0 t}\} It is periodic, with period T = \frac{2π}{\omega_0} Now consider g(t) = e^{-\alpha t} It is transient, with a time constant \tau = \frac{1}{\alpha} So...

For simplicity, you could consider a one dimensional case: \frac{dx}{dt}=v(x) This is a separable differential equation, so: \int_{x_0}^{x_f}\frac{dx}{v(x)}=\int_0^T dt But it gets you a solution for the final time, T. T = \int_{x_0}^{x_f}\frac{dx}{v(x)} If for a fixed x0, you...

Consider two blocks with masses m1 and m2 placed side by side on a frictionless surface. _-F->__|m1||m2|____ If there's a horizontal force F applied to m1, and m1 and m2 remain in contact, then the blocks will be accelerating together, as if they were one object with a combined mass...

An even function has the property: f(-x)=f(x) An odd function has the property: f(-x)=-f(x) Suppose you have a function f(x) that is neither odd nor even. Now, define a function g(x)=\frac{f(x)+f(-x)}{2}. So that, g(-x)=\frac{f(-x)+f(-(-x))}{2}=\frac{f(x)+f(-x)}{2}. This means...