0
$\begingroup$

I am having an issue understanding this mathematical modeling of an electromagnetic braking system.

I have this equation where z is the position and t the time,

$\frac{d^2z}{dt^2} = g - \frac{RL\lambda^2}{am\pi} \frac{z^2}{(z^2+4a^2)^5} \frac{dz}{dt}$

$\frac{d^2z}{dt^2}$ as far as I understand is the acceleration.

What I don't understand is why the acceleration (second derivative) is defined in terms of the velocity (first derivative)?

I am trying to graph the acceleration over time but I can't because I don't know the equation for velocity.

I hope I made myself clear; I'm having a hard time with this assignment.

Improve this question
$\endgroup$
5
  • $\begingroup$ You need to learn MathJax to show equations. I would edit this for you, but I'm not sure what the equation is. $\endgroup$
    – Bob D
    Commented Jun 9, 2021 at 20:49
  • $\begingroup$ @BobD thank you! i've edited it $\endgroup$
    – moonlight-hollow
    Commented Jun 9, 2021 at 20:53
  • $\begingroup$ Velocity is the first derivative of position with respect to time and acceleration is the second derivative of position with respect to time because acceleration is the rate of change of velocity. What is it you don't understand about that? $\endgroup$
    – Bob D
    Commented Jun 9, 2021 at 20:57
  • $\begingroup$ the title says "braking", thus terms which reduce velocity are sometimes proportional to the velocity itself, check a free-falling ball, its speed is reduced to a limiting value due to a term proportional to the velocity (sometimes squared). $\endgroup$
    – Nelson Vanegas A.
    Commented Jun 9, 2021 at 21:00
  • $\begingroup$ Try to get the dimension of each term in right hand side. You’ll get the dimensions of acceleration. So yes it is possible to definite it that way. $\endgroup$
    – Natru
    Commented Jun 10, 2021 at 5:55

2 Answers 2

Reset to default
0
$\begingroup$

You also don't know how position changes over time and you need both, velocity and position, to plot your graph.

The equation you wrote is differential equation and need to be solved first for function z(t), possibly by numerical methods. Once you know this, you can compute your derivatives you are interested in and plot them in a graph.

Improve this answer
$\endgroup$
0
$\begingroup$

It is hard to know without properly defining all the terms in your question and possibly a sketch to go with.

However, I should imagine it is due to Faraday's law of induction. The rate of change of magnetic flux in the electromagnetic braking system will then be proportional to the velocity of the carriage (I'm assuming this is an elevator question as you have $g$ the acceleration due to gravity.), this will provide a braking force which decelerates the carriage.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.