The circuit to be analyzed is shown below:
Since initial conditions are zero (from the instructions) I will use laplace transforms for the cirucit and I will use the MAME method to solve this circuit. The laplace transforms that are required will give me:
$$E_g(s) = \frac{10}{s}$$
$$ L_3...
In Mathematical Methods in the Physical Sciences by Mary Boas, the author defines the Laplace transform as...
$${L(f)=}\int_0^\infty{f(t)}e^{-pt}{dt=F(p)}$$
The author then states that "...since we integrate from 0 to ##\infty##, ##{L(f)}## is the same no matter how ##{f(t)}## is defined for...
By using the laplace transform:
$f(t)=sin(Φ(t))$
I want it in the form:
F(S)/Φ(S)
The purpose is to linearize it in order to put it into a larger transfer function, so far my only solution is to simplify it using taylor expansion.
What is the preferred method of measuring how accurate the normal approximation to the binomial distribution is? I know that the rule of thumb is that the expected number of successes and failures should both be >5 for the approximation to be adequate. But what is a useful definition of...
1. Homework Statement
The input signal of the circuit shown below is ##x(t)=2\sin (ω_ot + \pi/6)##. The switch in the circuit is controlled with a digital signal of the form ##s(t)=\sum_{k=-\infty}^{+\infty} (u(t+ε-kT_s) - u(t-ε-kT_s))##, ##\frac{2\pi}{T_s}=800\pi##, ##ε\to 0##, so that when...
If a Laplace transform has a region of convergence starting at Re(s)=0, does the Laplace transform evaluated at the imaginary axis exist? I.e. say that the Laplace transform of 1 is 1/s. Does this Laplace transform exist at say s=i?
1. Homework Statement
The switch in the circuit in has been closed for a long time. At the switch is opened. a) Find i0 for t>=0 (b) find v0 for t>=0
I don't understand the effect of the switch in the position it is in. It's acting as a short circuit, I think, so presumably the capacitor...
1. Homework Statement
The stability of a spinning body may be explored by using equation (3.40), with no
torque components present. It will be assumed here that the spin is about the z -axis and
has a rate ωZ = S.
2. Homework Equations
$$I_{xx}\dot{ω} - (I_{yy}-I_{zz})Sω_y = 0$$...
Hello,
I am studying control theory. And I have encountered something I have never considered or thought about.
Consider a system with y as the output differential equation and u as the input.
any(n) + ... + a1y(1) + a0y = bmu(m) + ... + b1u(1) + b0u
Here, the subscripts indicate...
Hello,
I have begun to teach myself Control Theory.
I am looking for a book that is focused for mechanical engineers. I do not mind examples in electrical engineering, but they bore me (no offense).
Also, I find some books begin with Laplace Transforms. Yet I found this online lecture...
1. Homework Statement
I'm trying to solve Laplace's equation numerically in 3d for a charged sphere in a big box. I'm using Comsol, which solves using the finite elements method. I used neumann BC on the surface of the sphere, and flux=0 BC on the box in which I have the sphere. The result does...
1. Homework Statement
I am given this equation:
and asked to solve using Laplace transforms
3. The Attempt at a Solution
This is what I did:
This seemed logical to me, I used partial fractions and it stayed pretty simple.
This is what the solutions my prof posted do:
Is my answer...
1. Homework Statement
2. Homework Equations
I'm studying a mathematical behaviour of a servo motor and I need some help to understand it.
The output signal is \$\beta (t)\$, representing the angle rotated by the axis at instant t, in relation to the equilibrium position.
On the servomotor...
1. Homework Statement
am trying to solve this PDE (as in the attached picture) https://i.imgur.com/JDSY4HA.jpg also my attempt is included, but i stopped in step, can you help me with it?
appreciated,
2. Homework Equations
3. The Attempt at a Solution
my attempt is the same as in the...
A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that.
However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation.
And then there are words like: harmonics (for higher...
1. Homework Statement
3. The Attempt at a Solution
As you can see, the answer is given in the problem. I have the 0.8t par right but somewhere along the way I messed up. I'm not really to sure about how to solve these types of problems using Laplace. Is there a general procedure that I...
1. Homework Statement
A beam is supported at one end, as shown in the diagram (PROBLEM 11 page 281 of Lea, 159 of the course pack). A block of mass M and length l is placed on the beam, as shown. Write down the known conditions at x = 0. Use the Laplace transform to solve for the beam...
I'm having trouble solving the differential equation (a-bx)y'+(c-dx)y-e=0 with a,b,c,d,e constants.
I tried laplace transforming it, but then I end up with yet another differential equation in the laplace domain because of the xy and xy' terms.
1. Homework Statement
Deriving an s-domain equation for the following inputs a) &b)
3. The Attempt at a Solution
I understand how to derive the equation for an input with zero initial conditions (part a) but I'm not sure what to do when there are non-zero initial conditions (part b)
Hi.
I read this thread with great interest and have similar question:
In a deterministic universe, does entropy exist for Laplace's demon? Since he knows the universe to it's microstate, does the term "macrostate" even make sense to him?
And say there is a "half-demon" that only knows the...
1. Homework Statement
I have the second order diff eq:
Solving by Laplace transform gets me to:
I could use the inverse laplace transform that takes me back to e^{at}cos(bt) with b=0, but that only solves for the homogeneous (complementary) part of the equation, it won't reproduce the...
1. Homework Statement
We want to find the Laplace transform for
f(t): 0 for t≤2 and (t-2)2 for t≥2
2. Homework Equations
I know that Lap{uc f(t-c)} = e-csLap{f(t)}=e-csF(s)
I rewrite f(t)=0+g(t) where g(t) = 0 for 0≤t<2 and (t-2)2 for t≥2
so we can write f(t)=g(t)=...
Hey guys :)
So I'm looking to form equations that I can apply a Laplace transformation to. The mechanism specifically is a trailer jack - it converts rotational motion to linear motion. And its high torque provides a mechanical advantage to lifting heaving loads.
Can anyone help me form...
Hi everyone,
I'm looking for a reference book that treats the theory behind the eigenfunctions solution of the so called vector Helmholtz equation and its Neumann and Dirichlet problems.
I've already found a theory inside the last chapter of Morse & Feshbach's Methods of theoretical physics...
1. Homework Statement
Given that r(t) = L^-1 (Inverse laplace) *H(S) and by making the link between the time-domain and frequency-domain responses of a network, explain in detail why the ideal “brick-wall” lowpass filter is not realisable in practice.
2. Homework Equations
3. The...
The equation is Uxx + Uyy = 0
And domain of solution is 0 < x < a, 0 < y < b
Boundary conditions:
Ux(0,y) = Ux(a,y) = 0
U(x,0) = 1
U(x,b) = 2
What I've done is that I did separation of variables:
U(x,y)=X(x)Y(y)
Plugging into the equation gives:
X''Y + XY'' = 0
Rearranging:
X''/X = -Y''/Y = k...
My homework problem is as follows:
Consider the Laplace transform shown below.
(4s3+15s2+s+30)/(s2+5s+6)
a. What is the value of f(t=0) and f(t=∞)? Use the initial and final value theorems.
b. Find the inverse transform f(t). Use this expression to find f(t=0) and f(t=∞) and compare with the...
bear with me, i know that this question has been asked many time , but i would like a definite answer, now, starting off the external charge density on the outer surface of sphere WILL be uniform by unique solution of Laplace equation and letting the sphere be huge, so, electric field due to...
1. Homework Statement
I know for t[u(t)-u(t-2)], we can simplify that to tu(t)-((t-2)+2)u(t-2) which then gives us tu(t)-(t-2)u(t-2)-u(t-2). Now, the laplace transform seems trivial but I am having problems with this equation:
sin(t)[u(t)-u(t-pi)]
2. Homework...