Questions tagged [mathematics]

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Maximum Deflection for simply supported beam under arbitrary triangular loading

I am trying to get the: maximum deflection location of maximum deflection deflection at any point For a beam under an arbitrary triangular load (i.e. a, b, c, and w can vary). I tried to solve this ...
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3 answers
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Use of 'parameter' in engineering?

Is there a different meaning to the word of 'parameter' in engineering? I've started in engineering from a mathematics/physics background, and commonly a 'parameter' is either used to 'parameterize' a ...
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1 answer
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Timoshenko Fixed Fixed Total Beam Deflection

I am trying to solve a problem where there is a fixed-fixed (clamped-clamped) beam with a point load in the middle (at L/2). The L/H is less then the 10 required for normal beam bending analysis and ...
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2 answers
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Why $\frac{m}{V}$ gives average density when density varies?

This might be a very basic question, and for years I have gone by simply accepting it as a fact. That whenever the density is uniform the formula $\frac{m}{V}$ gives that uniform value of density and ...
1 vote
3 answers
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Why stopping at the first derivative in conservation equations?

Oftentimes we, as engineers, have to write energy/mass/momentum balances to derive the governing equations for a quantity $\phi(x,t)$ of a physical system. One of many derivations of such balances ...
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Why are square Intergrable functions bounded? How is it related to L2 functions and Hilbert spaces?

To approximate the weak form of linear elliptic pde to solve Elasticity problem, we use L2 functions and Hilbert space. In that, I read that Square integrable functions are bounded. Why is that true ...
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2 answers
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How to analyze strongest (honeycomb?) structure?

To be specific I have a structure consisting of a solid material (eg PLA) consisting of a top horizontal slab (eg 3 cm x 3 cm x 0.5 cm) and a bottom horizontal slab (translated vertically, of the same ...
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How to calculate the degrees of freedom, constraints and the generalized coordinates in this dynamic system

The rope lengths are taken to be constant. Solution: $N$ particles with $k$ constraints. . Then the Degree of Freedom (DOF) is $3N-k$. In Figure 1, we have two particles $m_1$ and $m_2$, so $N=2$. But ...
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How to show that the infinity norm obtained in the problem given below is correct?

I found the following example problem in page 178 of the book "Nonlinear System" by Hassan K. Khalil, Third Edition. The objective of this problem is to show whether a system is input-to-...
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How to calculate scaled speed

While working on a project I faced a difficult problem. Let's say I have car at a 1/10 scale. Now if a real car drives at 10 m/s, it would take 3 seconds to travel 30m. If we look at the scaled car ...
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Calculations of a sphere

I apologize if the question is very basic, I admit I'm not the best at math and physics. I am doing an experiment with a sphere, the measurements are as follows: The sphere has a diameter of 330 mm (...
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1 answer
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Can the Dynosheet be read as a Fourier transform of some sorts?

I've done some quick google search on dynosheet, and what it does is that it measures the power output of the car with respect to its frequency. My initial understanding of the dynosheet is that it ...
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How to Determine a Valid Relationship Equation Between Two Finite Datasets -- Python, Matlab or Other [closed]

I struggled to find a clear solution online so I'm resorting to asking a fresh question. I have two finite datasets (call them 40x1 vectors) that are equal in length and generate non-linear curves, ...
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deal with algebraic loop in distributed control algorithm

Recently I found a distributed control method for multi-agent system, which implements an algebraic loop like: $$ u_{i}=(l_{ii}+b_{i})^{-1}\left [{\sum _{j\neq i}a_{ij}u_{j} -\mu e_{2i}+b_{i} u_{0} }\...
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3 answers
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Should I use the rounded values given on technical drawings or work at the highest reasonable resolution?

In the image, the table of dimensions only gives a resolution of 1mm; in the actual creation of such a sign, would these approximate values be used or their true values (within reason)? For example, R ...
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Piston that produces equal amounts of swing in a lever?

I am attempting to figure out an equation I've found for designing part of Walschaerts Valve Gear. The specific implementation isn't relevant here, because it's the math I'm after, but this is the ...
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1 answer
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Path length of a satellite signal

I am trying to work out the length of the Rsv, but I dont understand how to go about this. If the length R is known and the angle EL is known how do I go about solving for this length. I was given ...
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General Units question

so let’s say I worked out a quantity that turned out to be unit less but to work it out I used pounds (lb) and feet (ft) and the units cancelled out But then I used this unit less number later in ...
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2 answers
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Calculating two diagonal forces

When I tried to calculate the force exerted on the rope 'a' I get that it is equal to 5N when the block has a force of 10N. Do I instead need to divide by 30 since the sum of the two angles is 30 ...
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Temperature distribution using Laplace transform

Consider room that occupies quarter space That is formed by two walls. One wall is fully insulated and has a constant temperature $0$. Another wall has a window of length L that with one edge at the ...
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2 answers
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Calculating Torque With a Second Arm Attached to the Main Arm

I am working on some code that will handle the arm of a robot, and I want to be able to hold the arm in place against the force of gravity. The arm is in 2 parts just like a human arm and I intend to ...
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2 answers
390 views

Solving Timoshenko beam equation for cantilever beam

Update with solution Solution 1 Problem: Beam clamped at left side, free end on right side, point load pointing downwards. x is defined positive from the clamped end towards the free end. Create FBD ...
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Inside/outside test of any point on 2D plane?

Suppose I have one plane $Ax+By+Cz+D=0.$ I want to test $(x, y, z)$ is inside of this plane or outside. My attempt:1 Then draw normal N on that plane which point away from the observer Image1. If $Ax+...
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Automatic Tissue Dispenser

My father is a software engineer and yesterday he asked me a question to test me, that I cannot, for the life of me, seem to figure out. He told me that I need to make a tissue paper dispenser that, ...
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1 answer
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Calculate effect of drag on ball in motion

So I’ve been trying to work out the range of a ball that has been projected by two spinning discs please when accounting for drag- This is what I got so far: $V=V\cos\theta$, $T=2V\sin\theta/g$ , and $...
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How to calculate forces for most appropriate electric engine for soft sand? [duplicate]

I'm super new to this topic I'm posting here so please forgive the nursery question and content. I'm hoping to use any answers to help me begin my research and investigation on what I need to learn. I'...
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Is there an equation that can automatically tune a PID controller?

Is there an equation that can automatically tune PID controllers? or do I have to do manually/make an AI to do it for me?
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2 answers
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Is pursuing a Maths degree useful in engineering [closed]

whilst this is an open ended question, and not really 'on topic' for the site, I couldn't figure anywhere better to post it than on an engineering forum! (I can delete it after I receive an answer if ...
4 votes
4 answers
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How can I map a global spherical position of a central normal vector to the rotation of 2 perpendicular motors?

I have a machine that rotates two concentric frames. The outer frame has a motor that rotates it relative to the global y-axis, and the inner frame has a motor that rotates it about the outer frame's ...
2 votes
1 answer
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Raise/Lower 350lb Sawmill Head 12v Motor Specs

I am new to this site and have a problem to solve in an area that I’m pretty lost in. I can usually figure stuff out with the help of the internet and some digging but not getting real traction so ...
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Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x

I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system. i.e. $$ \dot{x}(t) = Ax(t) $$ is stable ...
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Can you offer real-world examples of logarithm use? [closed]

Can you offer real-world examples of logarithm use? An example of a real-world layman application of logarithms is understanding amplifier power ratings. For example a 30 watt amp is not one third as ...
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1 answer
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How do rollercoaster designers calculate the ideal curve?

I've been looking into rollercoaster track designs and wondered how they mathematically calculate the ideal curves to fit some specific layout without creating excessive Gs or other rider discomfort ...
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Resolving the forces into components [closed]

okay so I am really struggling to see how to resolve the Normal reaction force and Weight into the r and theta direction please? Why is it that the angle is taken to the left of N and right of mg ...
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1 answer
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Question regarding the extreme wind velocity distribution in Eurocode

Above is the definition of the probability factor from Eurocode 1-4. It is used in context of calculating the extreme wind load on a building. Ignoring some other factors, it is used as follows: $$v_b ...
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1 answer
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FE Exam practice: "How many years until you're a millionaire?" [closed]

One of the early questions in the NCEES FE Industrial/Systems Exam studyguide has a solution that I can't decipher. The question is as follows: ...
1 vote
1 answer
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Infinitesimal Strain Tensor in Cylindrical Coordinates

How can I obtain the below formulas of infinitesimal strain in cylindrical coordinates using matrix calculation given the first formula? I find it hard to study them because I still don't know how to ...
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1 answer
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Stretch in Infinitesimal strain theory

In the picture above we have the expression of stretch with respect to strain tensor, but in case of infinitesimal strain theory, we take stretch equal to 1+T.E.T I don't understand why by taking ...
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2 answers
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What's the name of the calculus used to make smooth transitions in roads?

So I'm not actually an engineer, I'm a novice computer programmer but I think in order to solve a problem I have I'm going to need some help from the world of engineering. I remember in high school ...
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Determine the parameters for this given nyquist plot

I have seen quite many of this type of question and I want to find how to solve them but I haven't cracked it yet. For example this is one: My thoughts so far: Replace $$s \rightarrow j\omega$$, $$G(...
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Could tic-mark labels on a graph have individual decimal digits with different signs?

I'm currently looking at a graph (figure 5 of Ede (1967), "Advances in Free Convection", in Hartnett and Irvine (eds.), Advances in Heat Transfer vol. 4, New York: Academic Press), in which ...
1 vote
3 answers
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Statically determinate system

The exercise is taken from linear algebra and its applications, prof. G. Strang Exercise 2.4.8 Truss I have already found that: m=n=8 → system is statically determinate, therefore solvable by ...
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1 answer
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Obtaining equation from real life

As I was studying about differential equation,then I got a question in my mind that we are taking out general solutions for a differential equation. Like for example - Q) $\frac{dy}{dx} = \left[\frac{...
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How to judge the character and sign of a dislocation?

I do understand that $ \mathbf b||\mathbf t$ for screw dislocation but I am unable to judge the sign of the dislocation. Again if $\mathbf b \perp \mathbf t$ how do I judge its sign? Any formula which ...
1 vote
2 answers
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Is there any application of control engineering to the study of algorithms stability or computer science theory?

I am an undergraduate student in Electrical and Computer engineering. In our 5th semester we have a obligatory "Introduction to control systems course". I was wondering if these bunch of ...
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2 answers
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How to Derive the Differential Form of the Contintuity Equation

The book "Gas Turbine Engineering Handbook" by Boyce, on p. 117 states, the continuity equation, $ \dot m = \rho A V $, has as its differential form, $ 0 = \frac{d\rho}{\rho} + \frac{dA}{A} ...
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Are gas distribution networks tree-like?

I was wondering, if it is justified to say, that gas distribution network graphs (primarily in Europe) are typically tree-like. By gas distribution networks I mean municipal and regional distribution ...
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1 answer
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How to calculate the torque for motors for a Core XY movment?

I am trying to design a simple setup that follows the core XY movement shown: I have been researching the statics behind this movement in order to calculate the minimum torque for the motor so I ...
3 votes
2 answers
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How high will a flywheel catapult launch a payload?

First off, this is not a homework question or anything like that. I'm trying to build a catapult to launch a payload using a flywheel as an energy device! It goes like this: The flywheel spins up to ...
1 vote
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multidimensional function for object description

I want to simulate a bow tie antenna and build it up with a function. so far i have managed to create a piece of cake with sin and cos. Now I would like to expand the function and round off the ...
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