Calculating Time Constant for First-Order Instrument Step Change

Click For Summary

Discussion Overview

The discussion revolves around calculating the time constant for a first-order instrument subjected to a step change in input. Participants are exploring the appropriate formula to use for this calculation and addressing issues related to the expression of the formula.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant presents a problem involving a first-order instrument and a step change of 100 units, seeking guidance on the correct formula for the time constant.
  • Another participant suggests a formula for the time constant, stating it as x(t) = A(1 - e^{-t/T}), where x(t) is the value at time t, A is the final value, and T is the time constant.
  • A later reply expresses a concern about the formatting of the formula in LaTex, providing it in text form as x(t) = A(1 - exp(-t/T)).

Areas of Agreement / Disagreement

There is no consensus on the correct formula for the time constant, as participants are still discussing and clarifying the expression of the formula.

Contextual Notes

Participants have not resolved the issue of the correct formula for the time constant, and there may be assumptions regarding the parameters involved that are not explicitly stated.

the_d
Messages
127
Reaction score
0
The problem is for a first-order instrument exposed to a step change of 100 units. If after 1.2 seconds the instrument indicated 80 units, estimate the instrument time constant.

the problem I am having is chosen the correct formula for the time constant, any suggestions?
 
Physics news on Phys.org
the_d said:
The problem is for a first-order instrument exposed to a step change of 100 units. If after 1.2 seconds the instrument indicated 80 units, estimate the instrument time constant.

the problem I am having is chosen the correct formula for the time constant, any suggestions?
The formula is
[tex]x(t) = A(1 - e^{-t/T})[/tex]
where
  • x(t) is the value at time t
  • A is the final value
  • T is the time constant
 
  • Like
Likes   Reactions: 299
I don't know why my LaTex formula didn't work. Here it goes in text form:
x(t) = A(1 - exp(-t/T))
 
much thanks
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
Replies
60
Views
5K
  • · Replies 5 ·
Replies
5
Views
3K
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K