Recent content by END

Homework Statement Solve the following: $$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$ Homework Equations Table of Laplace Transforms.The Attempt at a Solution The solution is $$f(t) = (1/4 )e^{t/2} (\sin(2 t)+4 \cos(2 t))$$ I know I need to break up ##F(s)## into...

Thank you for the in-depth explanation to a numerical approach, TheoMcCloskey! The technique you outlined is just beyond my current mathematical level of understanding, but it's educating to see a technique like that in action, and it's definitely brought up some points to research. Does your...

I have the following system of equations with variables ##a,m##, and I'm wondering—can this system be solved symbolically/analytically? \begin{align} m &= 100 + \frac{ \left( 200 \frac{\ln{\frac{1}{2}}}{26.8} \right) }{\left(\dfrac{\ln{\frac{1}{2}}}{26.8} + a \right)} \\ \\ 50 &= me^{-a\left(...

Thanks for your response, mathman. Here are some resources that utilize this notation: (page 1) http://www.sut.ac.th/engineering/Civil/CourseOnline/430201/pdf/05_review.pdf Vector Mechanics for Engineers:Statics and Dynamics by Ferdinand P. Beer & E. Russell Johnston J. Below is an example...

In the context of centroids and moments, what do ##\bar{x}_{\textrm{el}}## and ##\bar{y}_{\textrm{el}}## represent? For example: $$\bar{x}L = \int \bar{x}_{\textrm{el}}dL$$

Thanks for your enlightening responses, Andrew!

Thank you, TitasB!

Hey, PF I'm reading the following derivation of least squares, and I'm trying to figure out how the author went from the last step at the bottom of pg. 7 to the final equation (11) at the top of pg. 8. [http://isites.harvard.edu/fs/docs/icb.topic515975.files/OLSDerivation.pdf] More...

Awesome explanation! That was exactly what I was trying to express, but you managed to say it more elegantly. I think I'm beginning to understand this problem at a deeper level now. By numerical techniques, I assume you mean we cannot apply symbolic techniques in those cases. I would also...

Thanks for the example and clarification, Stephen! So I suppose I used the wrong notation to express my question. It still seems to me that ##A(t)## and ##B(t)## can be use to express either ##B## or ##A## as an implicit function of ##t##. This would be my ##A## as a function of ##B## or vice...

Thanks for your responses, Fredrik and Andrew (I'm still trying to understand your post, Fredrik). I ran into function composition and decomposition while trying to understand this problem, and if I recall correctly, it seems like most function composition consists of substitution (which I...

Hey, PF: If I have a function ##f(x)## where ##x## is itself a function of another variable (say time), is the following then true? $$f(x)=f(x(t))=f(t)$$ I ask this because if I have the following system of differential equations $$\frac{dA}{dt}=-Bb$$ $$\frac{dB}{dt}=-Aa$$ where litte ##a##...

Thanks, Merlin! I'm glad I was on the right track. I was able to get the correct answers to the rest of the problem thanks to your help. Best!

Homework Statement a.) [/B]A proton and an "positron" (identical to an electron, except positively charged) are brought ##5µm## apart and released from rest. What is the initial potential energy stored by this system? b.) In all of the previous problems on this homework, the system's...

Thanks for the updated feedback, Simon. According to WolframAlpha, the DE is a first-order linear ordinary differential equation http://www.wolframalpha.com/input/?i=y%27%3Dxy Also, could you please define second order? Is the term in this given context synonymous with second degree?