15
votes
Accepted
Is radians a dimensionless quantity?
radian is a derived unit, defined as the ratio of arc length to radius. As the ratio of two lengths it is dimensionless.
- 959
12
votes
Accepted
How can I determine a function equation from a graph image?
I don't know how this function was obtained (or what it is supposed to represent). But you could try searching the literature to see if someone has published equations of the curves. However, looking ...
- 2,631
10
votes
Determine the moment of inertia of a filled circular sector
Consider an infinitesimal element of area $r d\theta dr$ which is at a distance $r \sin (\theta)$ from the $x$ axis.
Its moment of inertia is $r d\theta dr (r \sin (\theta ))^2$.
The moment of ...
- 1,951
7
votes
Variation of LED light as a function of distance
All EM radiation from a point source falls off in intensity with the square of the distance. LEDs can't magically change this basic physics.
LEDs can be quite directional in their emission pattern. ...
- 11.4k
7
votes
Accepted
Does every engineering design needs to have a complete theoretical backing or may experimental data suffice?
Are any designs based solely on data from trial and error used in critical mainstream engineering?
Usually not. And the reason is that trial and error is expensive and time consuming. As engineers, ...
- 2,646
6
votes
Differential equations of a (simplified) loading bridge
Kinematics and dynamics
Those are the steps to solve problems of this nature.
Analize the kinematics of the system.
$\hspace{5.em}$ $_{o}\vec{r}_{OP}$ = $_{o}\vec{r}_{OR}$ + $_{o}\vec{r}_{RP}$
$\...
- 122
6
votes
Accepted
How to Derive the Differential Form of the Contintuity Equation
for $y = f(x_1, ..., x_n)$, the sum of the partial differentials with respect to all of the independent variables is the total differential:
$$ dy = \frac{\partial y}{\partial x_1}dx_1+...+\frac{\...
- 2,160
5
votes
Accepted
Differential equations of a (simplified) loading bridge
My guess is that you probably need another differential equation for the angular movement, that will involve the inertia, such as:
$$m_G l^2 \ddot{\varphi} = m_G g l \sin(\varphi)$$
which yields:
$$...
- 1,831
5
votes
Accepted
Determine the moment of inertia of a filled circular sector
Since you actually asked for the moment about the $x$ axis. Calculating the moment of inertia about the $x$ axis is a fair deal more complicated than calculating it about the $z$ axis as in my other ...
- 6,386
5
votes
Derivation of the weak form for the euler-bernoulli beam equations
It's easier to understand this identity if you start with the partial differential equation for the Euler-bernoulli beam deflection equation
$$\frac{d^2}{dx^2}\left[ EI \frac{d^2u}{dx^2}\right] = 0$$
...
- 2,549
5
votes
Accepted
Square wave transfer function?
I thought I would expand a little on the answer offered by Karlo.
Long story short, I would not try to calculate the analytical time response of a system to a square wave. That would be a serious ...
5
votes
Accepted
Difference between partial derivatives and derivatives in physics
For a detailed explanation search WikiPedia for derivative, partial derivative and ...
- 540
5
votes
Is engineering basically controlling oscillators?
No.
First, there is much much more to most engineering disciplines than analyzing the response of something.
Second, even when that is part of the task, it isn't done by "adding oscillators", ...
- 11.4k
5
votes
Frequency Response of a Discrete System
If you want to evaluate a continues time transfer function at a specific frequency $\omega$ in rad/s you substitute $s$ with $j\,\omega$. For a discrete time transfer function you substitute $z$ with $...
- 1,653
5
votes
Should Engineers Understand Equations without Relying on Derivations?
Knowing the derivation is important because it usually tells you what initial assumptions were made in the derivation and what the limits of applicability of the resulting equation are. Understanding ...
- 14.3k
5
votes
Can you offer real-world examples of logarithm use?
Following are a few examples of logarithmic use. Some well know (like Richter and Decibel), some other more morbid (like pH, or spreading of diseases).
On each example, you could write a full answer, ...
- 24.3k
4
votes
Accepted
Uncertainty Calculation of LVDT displacement transducers for length measurement
For the Maths of calculating uncertainty the standard document is the GUM. Which describes all the maths but can be somewhat unclear if you don't already have some idea how it is supposed to work.
...
- 1,035
4
votes
Applications of the Laplace Transform
I think you are neglecting the broad range of applications included in solving 'some kind of differential equation.' At the very basic level of physics, everything we know about the world is ...
- 6,386
4
votes
How can I determine a function equation from a graph image?
You have a single-valued function dependent of two variables. There are many ways to model that.
If you know something about what this function represents, then going back to the physics might yield ...
- 11.4k
4
votes
Accepted
Help an electrical engineering student with a beam deflection question
Yes.
The first derivative of the deflection is equal to the tangent of the deflection, which for small deflections can be approximated as equal to the angle of rotation of the beam at each point.
...
- 13.1k
4
votes
Accepted
3D Transformation Between Two Cartesian Coordinate Systems Using Euler Angles
Suppose Frame 1 is a world coordinate frame and Frame 2 local robot frame.
The thing that's a little confusing here is that when you transform from Frame 1 to Frame 2, you are saying that you want ...
- 3,575
4
votes
Accepted
Should Engineers Understand Equations without Relying on Derivations?
Should I, as an engineer-in-training hoping to complete research, focus on trying to understand equations to my satisfaction, or should I instead just become well acquainted the equations, their use ...
- 2,878
4
votes
How can I implement S-curve motion profile on mobile robotic platform / wheeled robot?
There are many ways to create a trajectory between two points using a sigmoid function. It's not a simple question, and the math is a little involved. Here's how I would do it.
Short Answer
You can ...
- 1,220
4
votes
Swing safety: maximum load of beam (supported at one end, free with load on the other)
I would recommend you have your boys wear a helmet while playing. Also cover the landing area with 8 inch deep bed of mulch or some soft material like foam sheets covered by a mat.
With all due ...
- 22.1k
4
votes
Accepted
Stretch in Infinitesimal strain theory
Taylor is straightforward:
$$
\sqrt{1+2x}
=\left.\sqrt{1+2x}\right|_0
+\left.{d \over dx}\sqrt{1+2x}\right|_0x
+O(x^2) \\
=1
+\left.{d \over dx}{1 \over \sqrt{1+2x}}\right|_0x
+O(x^2) \\
=1
+x
+...
- 238
4
votes
Matrix Calculation
Your numbers are right. You are just confused about matrix multiplication. See https://en.wikipedia.org/wiki/Matrix_multiplication (or any linear algebra textbook):
For matrix multiplication, the ...
- 2,646
3
votes
Accepted
What is the first moment area of a rounded rectangle?
I don't have a simple formula but that is the way i would handle it. Assuming the four corners are circular with equal radius r, so that symmetry exists, the first moment of area of one half of the ...
- 347
3
votes
Accepted
Equating $\frac{dp}{dt}$ and $F$ at a hydraulic jump?
$F=\frac{dp}{dt}$ is, in some sense, a more fundamental expression of Newton's law than $F=ma$ because $F=ma$ doesn't allow for situations with changing mass. You can easily derive the second from ...
- 6,386
3
votes
Modifying a fixed camera lens for close focus
I think you are misinterpreting what your variables are. The focal length is fixed for a given lens and cannot be changed. What you can change is the image to lens distance. Combined these will ...
- 1,035
3
votes
Calculating the force and/or torque required to pivot an arm from one end
My calculation got the same answer as you. Here's what I did.
You mentioned that the arm has some weight so I added that force to your diagram. Also, I labeled the center of the elbow joint as ...
- 61
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