I am trying to design a water vessel system that maintains it's water level as it is consumed.
In item 1. It's a simple water barometer, where the height of water in the column can be supported by atmospheric pressure until 10.34.
In item 2. There are two columns that are open to atmosphere...
Homework Statement
An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window. A loudspeaker is located outdoors, 46 m away and facing the window. The intensity level of the sound entering the window space from the loudspeaker is 42 dB. Assume the acoustic...
Homework Statement
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use richardson extrapolation to estimate the first derivative y=ln(x), x=5 using steps of 2, 1, 0.5. Four decimal points. obtain true relative error for the last estimate and comment on its value.
Homework Equations
[/B]
deriv ln(x)=1/x
The Attempt at a Solution
I...
Homework Statement
Consider the initial value problem for the system of first-order differential equations
y_1' = -2y_2+1, y_1(0)=2
y_2' = -8y_1+2, y_2(0)=-1
If the matrix
[ 0 -2
-8 0 ]
has eigenvalues and eigenvectors L_1= -4 V_1= [ 1...
Homework Statement
If the method of undetermined coefficients is used to find a particular solution
yp (t) to the differential equation y'''-y'=te^(-t)+2cos(t) should
have the form: ?
Homework Equations
The Attempt at a Solution
LHS
r^3-r=0
roots= 0, 1
y_c(t)=c_1e^t
RHS...
Homework Statement
y''-y=t-4e^(-t)
Homework Equations
method of undetermined coefficients
The Attempt at a Solution
solving for characteristic equation first
y''-y=0
r^2-1=0
c_1e^(-t)+c_2e^(t)
RHS
particular solution
t-4e^(-t)
y_p(t)= At+B+Ce^(-t)
y_pt'(t)=A-Ce^(-t)...
Homework Statement
A uniform ladder having mass 14kg and length 3m is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle Theta at which the bottom end A starts to lift off the ground. For calculation assume the ladder is a slender rod...
Homework Statement
During a sustained wind the blades on a two blade horizontal–axis wind turbine is
turning with an angular velocity of 5 rad/s. If initially the blades have an angular velocity of 2
rad/s, determine the distance point P on the tip of the blade has travelled in 3.0 seconds...
Homework Statement
If y=y(t) is the solution of the initial value problem
{
y'+(2t+1)y=2cos(t)
y(0)=2
then
y''(0)=?
it is a multiple choice practice problem with choices
y''(0)=2
y''(0)=-2
y''(0)=4
y''(0)=0
y''(0)=-4
Homework Equations
The Attempt at a Solution
Im really not sure how...
Homework Statement
Find the general solution:
y'-3y=(y^2)
Homework Equations
The Attempt at a Solution
divide both sides by y^2
y'(y^-2) -3(y^-1) = 1
we know v=y^(n-1)
v=y^-1
v'=d/dx(y^-1)
v'=-(y^-2) y'
plug it back into
y'(y^-2) -3(y^-1) = 1
-v'-3v=1
this is where I think I am...
Homework Statement
Practice problem for midterm.
Homework Equations
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T_1+U_1=T_2+U_2
U_spring=1/2kx^2
The Attempt at a Solution
[/B]
Set X-axis along the 30 degree line and the Y-axis perpendicular.
I'm not sure how to consider the friction constant into the formula.
Any help is...
Homework Statement
Find all zeroes for the function f(x)
f(x)=x^3+25x
Homework Equations
The Attempt at a Solution
I tried factoring out x out of it.
x(x^2+25)
and again to give
x[(x+5i)(x-5i)]
this would give me the 0,-5i,+5i as the zeroes. Doesn't seem to be right though.
Any...
Can you calculate eigenvalues and eigenvectors for rotation matrices the same way you would for a regular matrix?
If not, what has to be done differently?
Homework Statement
We are looking for the matrix A
Homework Equations
(A^transpose)^transpose=A
The Attempt at a Solution
i would start with finding the transpose of the matrix.
-5 0
-8 -7
If a single photon light source shoots a photon through the "attached" path. What is the percentage of the photon will make it to each detector. The light source is the box, the photon trajetory is yellow, beamsplitter is blue, mirror is black, detectors are purple, and obstacle is red. I think...