Questions tagged [mathematics]

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10
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2answers
641 views

Differential equations of a (simplified) loading bridge

I am having trouble to calculate the differential equations of a simplified loading bridge. The system is build as shown in the picture below (just a sketch): If I use the Newton approach, I am ...
10
votes
1answer
609 views

Response of a system to a step function (Heaviside function)

I'd like to compute the response to a step function of a electrical/thermal system. Generally I can "easily" compute the transfer function $H$: $$H(\omega) = \frac{V_{out}(\omega)}{V_{in}(\omega)}$$ ...
9
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1answer
3k views

Derivation of the weak form for the euler-bernoulli beam equations

I am master student and doing an assignment of Finite element method. In the instruction I could not understand the derivation of the weak form, which should not be difficult. I'm sorry for posting ...
8
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3answers
2k views

How do I properly compute mean time to failure?

I have a product of which we have shipped something like 500 units over the last five years. This product is not intended to be user serviceable; a failure of any component results in the unit being ...
8
votes
1answer
200 views

What are the meanings of the second argument to the convolution?

I was trying to understand the convolution better and its mathematical properties and interpretations in engineering (specially in the context of computer vision). Recall the convolution: $$ s(t) = (...
8
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0answers
576 views

Incompressible 2D pressure-driven flow: for Navier-Stokes equations in nondimensional form, how should I express pressure boundary conditions?

*I have updated this question. I'm using two codes for modeling incompressible, two-dimensional flow out of a tank. My fluid dynamics experience is pretty basic; I'm using the codes to understand a ...
7
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4answers
341 views

Is radians a dimensionless quantity?

Quite often while calculating angular velocity we come across the quantity radians per second. How do I treat radian dimensionally?
7
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1answer
138 views

LED Lumen Calculations

I am using an LED as a point source for a school project. I have two questions in regards to the LED(s). I know that light follows the inverse square law when measuring perceived brightness, but all ...
6
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2answers
8k views

How can I determine a function equation from a graph image?

How can I find out the function equations in a diagram with 5 curves? Measuring by hand is very inaccurate and takes a lot of time. Any other possibilities?
6
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2answers
89 views

Does every engineering design needs to have a complete theoretical backing or may experimental data suffice?

This may sound rather vague on its own so I will explain with examples. The solid booster rockets used by NASA space shuttle used a central bore design because it had a certain characteristic on ...
6
votes
4answers
875 views

How can I calculate the rate of power consumption of a solar car along a known route with changes in elevation?

I am working on designing and creating a solar powered car for the Solar Car Challenge. The car will have to race from Dallas, TX to Minneapolis, MN in 5 days (~5 hours of driving a day) along back ...
6
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1answer
566 views

Differential equation of the vertical displacement of a cable

Given a cable (totally flexible) fixed at both ends, subjected to a vertical force $f(x)$ in his plane, with variable area $A(x)$, and variable elasticity $E(x)$ I want to find the differential ...
5
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4answers
576 views

Should Engineers Understand Equations without Relying on Derivations?

As I've progress through my undergraduate engineering program, I've noticed a shift away from physical intuition - understanding why certain phenomena or equations make sense because of basic patterns ...
5
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1answer
111 views

Equating $\frac{dp}{dt}$ and $F$ at a hydraulic jump?

A journal I am reading about circular hydraulic jumps provides the equation and I quote: $H$ Depth after hydraulic jump, $h$ depth before hydraulic jump, $V$ velocity after hydraulic jump, $v$ ...
5
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1answer
720 views

Discontinuity in mechanism simulation: is the mechanism jammed or is my analysis wrong?

I'm designing a compact mechanism for the deployment of a mast. The idea is that the linear actuator for the deployment is on the other side of the pivot, and a slider increases the lever arm to ...
5
votes
2answers
256 views

Why choose approximation over interpolation to implement digital lofting?

Before widespread use of digital computers lofting was done using a thin flexible strip, called spline, held in place by a series of weights. This technique is a type of interpolation (curve exactly ...
5
votes
1answer
510 views

How can I translate a pressure boundary condition to a velocity boundary condition for incompressible, viscous flow?

I have been working with an old code for modeling incompressible, 2D viscous flow out of a tank to understand a chemical process. There isn't much documentation and I'm not a fluid dynamicist, so I ...
5
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1answer
339 views

Shear Force Distribution on disk

I have to solve the differential equation for radial disks, and therefore I need the shear force distribution. The disk is rotationally symmetric. I want to use the superpositions principle and set 3 ...
5
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0answers
52 views

Is the viscosity solution of Hamilton-Jacobi equation of practical use in optimal control?

My understanding is, given an optimal control problem, one can show that the optimal cost satisfies a Hamilton-Jacobi PDE and use dynamic programming to figure out the optimal control. However, ...
4
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2answers
3k views

Determine the moment of inertia of a filled circular sector

Does anyone know how to determine the moment of inertia of the filled circular sector shown below? Apparently I have to use $dA=r\ d\theta\ dr$, $y= r\sin(\theta)$ and end up getting $I_x=\frac{r^4}{...
4
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2answers
1k views

3D Transformation Between Two Cartesian Coordinate Systems Using Euler Angles

I am trying to transform any arbitrary vector $\bf{v_{1}}$ in a Cartesian frame $\mathscr{F_{1}}$ into a different Cartesian frame $\mathscr{F_{2}}$. Both $\mathscr{F_{1}}$ and $\mathscr{F_{2}}$ have ...
4
votes
1answer
1k views

Uncertainty Calculation of LVDT displacement transducers for length measurement

I have to calculate the uncertainty of measurement for an LVDT Linear displacement transducer used for measuring length. Uncertainty calculations are ruled by ISO 17025 but there are no (at least ...
4
votes
1answer
78 views

Steady state value, a possible shortcut?

I have this differential equation: $\dot{\eta (t)}=\frac{-2\eta(t)}{C(\widehat{R}+\Delta R)}+\frac{K^2 L}{C E^2 (\widehat{R}+\Delta R)}+K$ which, my book says, correspond to a LTI system, ...
4
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2answers
4k views

How does one calculate degrees of freedom in a reactor with parallel reactions?

Some time ago, I was going through some exercises and I came across a odd question, for which my atomic species degrees of freedom did not match my degrees of freedom using molecular species. I showed ...
4
votes
1answer
171 views

Modifying a fixed camera lens for close focus

I found this article on hacking macro lenses. The author used a lens extension tube to allow closer focusing. IE The lens's Minimum Object Distance (MOD) was significantly reduced. I cannot find an ...
4
votes
1answer
50 views

How to apply static failure criteria for bending stress in an angled cylindrical surface?

Let’s say I have an irregularly shaped bearing with a cross section that looks like the angled surface of a conical frustum, shown below. If a bending moment is applied which causes the inside ...
4
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1answer
2k views

How to Calculate Mean Radius of Irregular Contact Face (Torque Transmission)

In a simple situation, one simply takes the average of outer diameter and inner diameter to gain the mean radius for calculating torque transmission through a contact face, such as a clutch. But how ...
4
votes
4answers
88 views

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 ...
4
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0answers
16 views

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 ...
3
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2answers
183 views

Frequency Response of a Discrete System

Let's say that I have the following continuous system: $$G(s)= \frac{2}{1+s}$$ I could convert it to a discrete system using for example the Tustin approximation https://en.wikipedia.org/wiki/...
3
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2answers
2k views

Square wave transfer function?

I made a mathematical model (transfer function) of a rlc circuit. I simulated it in matlab simulink with step input and square wave input and observed the result. I can also calculate this system with ...
3
votes
2answers
183 views

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 ...
3
votes
3answers
177 views

Calculate area of mesh?

I have expanded steel mesh that I use to make garden cages: I would like to know how much sunlight the mesh blocks. I think I need to calculate the area that the mesh takes up (per square inch) and ...
3
votes
1answer
1k views

What is the first moment area of a rounded rectangle? [closed]

I need to calculate the plastic section modulus of a rectangular section with rounded corners. First I need to know the formula for first moment area of a quadrant. I can't find it anywhere on the ...
3
votes
2answers
2k views

Second Moment of Inertia (or Second Moment of Area) of Beam Section

I need to calculate the moment of Inertia Iyz but I find 0 information online about how to get it or solve it in a real problem, only that is equal to $$\bar{I}_{yz}=\int yz\text{ d}A$$ How can I ...
3
votes
1answer
65 views

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 ...
3
votes
2answers
277 views

How to calculate rotations from displacements?

I'm trying to develop a finite conical shell element with six dof at each node. I want to express the rotations $\phi$, $\theta$ and $\psi$ in terms of the displacements $u$, $v$ and $w$. The ...
3
votes
0answers
42 views

How does NASA's QueSST X-59 jet work?

The QueSST (Quiet Supersonic Transport) is a project to create a more diffuse sonic boom in order to use supersonic flight commercially without the usual abrupt 1~2 psf pressure spike damaging the ...
3
votes
0answers
48 views

Mathematical transformation of a heading angle to a roll angle

I'm trying to understand a function in a SIMULINK example of a path following UAV simulation. The gist is that, the UAV Waypoint Follower block provides a required heading from a list of waypoints and ...
3
votes
0answers
216 views

How to integrate ∫vᵢ(uᵢ² + vᵢ²)dA in calculating monosymmetry index of an angle?

I saw this question asking about calculating monosymmetry index of an unequal angle. What I need is a formula to calculate $\int v_i{(u_i}^2 + {v_i}^2)\text{d}A$, given the depth $d$, breadth $b$ and ...
3
votes
1answer
787 views

Custom heavy gauge machine table to support clothes dryer

Background Looking to build a table for a dryer to fit inside a laundry closet. The table must be assembled inside the closet, as such it has three parts: two legs and a metal sheet for the table top. ...
2
votes
4answers
146 views

Swing safety: maximum load of beam (supported at one end, free with load on the other)

My husband and his dad built a fort for our two boys. Coming off of one side of the fort is a 4x6 wooden beam with a tire swing attached at the end. It is supported on one side by the fort, but not ...
2
votes
4answers
80 views

Planes, lines and distances: looking for engineering problems

In a week from now, I am going to teach a one-time class to first-year engineering students about 3D geometry, more specifically: distances between points and lines/planes, and the common ...
2
votes
3answers
107 views

Is there any defined mathematical parameter that can give me the average distance of a volume to a point?

I'm currently trying to design a bulk-handling system which minimizes the distance from the bulk material pile(s) where the material is loaded (the volume) to the unloading platform(s) (the point), ...
2
votes
1answer
1k views

Help an electrical engineering student with a beam deflection question

The theoretical formula for my beam deflection is: $ v(x) = \begin{cases} -\frac{Px}{48EI}(3L^2-4x^2), & 0\le x \le {L\over2}\\ -\frac{P(x-L)}{48EI}(L^2-8Lx+4x^2), & {L\over2}\lt x \le L \...
2
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1answer
4k views

Applications of the Laplace Transform [closed]

I have heard it said that the Laplace transform has "many applications". But the only "applications" that I ever came across are those that require one to solve either some kind of differential ...
2
votes
1answer
142 views

Help understanding a control system represented by coefficients of theta?

I've been working with control systems and transfer functions recently, but I've come across a format that I haven't seen before using coefficients of theta, and I can't find any information about it. ...
2
votes
1answer
87 views

Input-output representation to state space

How do you create a state space representation of the following input/output equation: $$ \dot{y} = -ky + u + a\sin(ωt) $$ where the parameters $k$, $a$, and $ω$ are unknown. The end goal is to ...
2
votes
1answer
170 views

linearizing a non linear state space equation

I have this 1-DOF helicopter simulator. The motor's armature resistance is $R$, inductance $L$ and motor constant $K$ and reaction torque on the motor shaft is $τ$. $T$ is equal to $k_1w_2^2$ and $...
2
votes
1answer
110 views

What exactly is a proportionality?

I thought I understood what a proportionality was, but it was recently called into question. I want to make sure I fully understand how the term is generally used in the engineering world. The basic ...