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:
$$\bar{x}L = \int \bar{x}_{\textrm{el}}dL$$
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##...
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?
In my multivariable calculus class, we briefly went over Taylor polynomial approximations for functions of two variables. My professor said that the second degree terms include any of the following:
$$x^2, y^2, xy$$
What surprised me was the fact that xy was listed as a nonlinear term.
In...
Thank you for your replies!
You were right; each field line represents an equal fraction of the original charge. The answer came out to around $$-7.1 \mathrm{C}$$.
Homework Statement
The electric field map is shown below. (Take it to be a self-consistent scale drawing at a particular moment in time.)
where \mathrm{q}_4 = +10 C, \mathrm{q}_6 = +10 C
What is the charge of \mathrm{q}_5 ?
Homework Equations
The Attempt at a Solution
I've tried the...
Have you tried:
http://en.wikipedia.org/wiki/Friction ?
"Friction is not itself a fundamental force but arises from interatomic and intermolecular forces between the two contacting surfaces. "
Homework Statement
A point charge q =+6.4 \mu \mathrm{C} is placed at each corner of an equilateral triangle with sides 0.29 \mathrm{m} in length.
What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle?
Hint: if you are careful to examine the...
What's the best approach to solving the partial-fraction decomposition of the following expression?
$$\frac{1}{(a-y)(b-y)}$$
The expression is not of the following forms:
But I know the solution is
$$= \frac{1}{(a-b)(y-a)}-\frac{1}{(a-b)(y-b)}$$
The problem statement
The solutions of ##NaC_2H_3O_3 + BaCl_2 +NH_4NO_3 + K_2CrO_4## are mixed together.
1. Write the Net Ionic Equation.
2. What is the driving force of the reaction?
The attempt
I'm not sure how to solve for the net ionic equation without a balanced equation. My...
1. The problem
A 3.0-kg block sits on top of a 5.0-kg block which is on a horizontal surface. The 5.0-kg block is pulled to the right with a force ##\overrightarrow{F}## shown in the figure. The coefficient of static friction between all surfaces is 0.65 and the kinetic coefficient is...
Homework Statement
The problem:
Two blocks made of different materials connected together by a thin cord, slide down a plane ramp inclined at an angle θ to the horizontal as shown in the figure (block B is above block A). The masses of the blocks are mA and mB and the coefficients of...
I think I see where you're going. Should the vertical component of one side of the rope be halved because the total weight ##T_y=735N## is being split/shared between the two sides of the rope?
If so, I get the following:
$$arcos(\frac{367.5N} {3000N})\approx 82.96^{\circ}$$
$$\Rightarrow...
Thanks for the feedback, SteamKing.
Looking back over my work, I believe I found the vertical component in the rope as
$$T_y=mg\rightarrow 75.0kg\cdot 9.8\frac{m}{s^2}=735N$$
Is this incorrect?
If not, knowing that the total tension ##\|\vec{T}\|## must be
$$\|\vec{T}\|\leq3000N$$
for one...
Thanks, Jim.
So would ##H_2TeO_4\cdot2H_2O## then be considered a hydrate due to the presence of water molecules within it?
In addition, how are we supposed to know that telluric acid is a hydrate? (i.e., that it has a ##nH_2O##)
Homework Statement
Christian is making a Tyrolean traverse as shown in the figure. That is, he traverses a chasm by stringing a rope between a tree on one side of the chasm and a tree on the opposite side, 25m away. The rope must sag sufficiently so it won't break. Assume the rope can...
According to Wikipedia, the proper chemical formula for Telluric Acid is Te(OH)_6.
From what I've learned in chemistry thus far, acids made from polyatomic ions within the same group follow a similar pattern. For example, Selenic Acid H_2SeO_4 is analogous to Sulphuric acid H_2SO_4. If this...
Thank you, ehild.
You were correct in stating that A and C cannot be solved, and I was able to compute the average acceleration by breaking the vectors into their components.
Homework Statement
A car is moving with speed ##17.4m/s## due south at one moment and ##28.3m/s## due east ##7.50s## later.
A. Determine the magnitude and direction of its average velocity over this time interval.
B. Determine the magnitude and direction of its average acceleration over...
Ah, bounded was the word I was looking for! Thank you, Stephen.
Would the example then be considered a Truncated normal distribution ?
If this is the case, what would 2.5 or 3 standard deviations imply in relation to the three-sigma rule when the values simply cannot extend beyond the...
Hello, PF!
[My question pertains to a non-rigorous, undergraduate introductory Probability and Statistics course. I'm no math major, so please correct me if I've mishandled any terms or concepts as I try to express myself. I'm always eager to learn!]
* * *
In a discussion of the...