Need Help about Deriving Radical.

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    deriving Radical
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Discussion Overview

The discussion revolves around the derivation of the formula T = 2π√(m/k) to express k in terms of T, m, and π. Participants are exploring the algebraic manipulation required to achieve the transformation to k = 4π²m/T².

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant seeks clarification on how to derive k = 4π²m/T² from T = 2π√(m/k).
  • Another participant suggests isolating the square root as a first step but does not provide a specific method.
  • A participant expresses uncertainty about their approach to removing the radical and questions if their steps are correct.
  • One participant explains the general principle of isolating variables by dividing or squaring, relating it to the original equation.
  • Subsequent replies indicate a progression in understanding, with one participant correctly applying the steps to manipulate the equation, while another points out a potential typo in the notation used.

Areas of Agreement / Disagreement

Participants are generally engaged in a collaborative effort to understand the derivation, but there is no consensus on the specific steps or notation, as some express confusion and others clarify points.

Contextual Notes

There are unresolved aspects regarding the clarity of notation and the correctness of the initial steps taken by participants. Some assumptions about algebraic manipulation are not explicitly stated.

KevinPaul06
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I'm trying to derive T= 2π√m/k to become k= 4π2m/T2

How is that happen? Can someone please explain it to me? Thanks in advance!
 
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So you're starting from:

[tex]T = 2n \sqrt{\frac{m}{k}}[/tex]

The first step would be to isolate the square root. How do you do that?
 
I don't know. I tried to this T=2π (m/k)1/2 to remove the radical. I don't what's next and I'm not even sure if that is really the 1st step.
 
If you have c= ab and want to "isolate" b, divide both sides by a: b= c/a.

If have a square root, [itex]y= \sqrt{x}[/itex], square both sides: [itex]x= y^2[/itex]

In both cases we are "undoing" what was done by doing the opposite. In "c= ab", b is not isolated because it is multiplied by a. The opposite of "multiply by a" is "divide by a". The opposite of square root is the square.
 
Okay thanks I think I get it.

T= 2π√m/k

(T/2π)2 = √m/k

T2/4π2 = m/k

T2/4π2m = 1/k , then reciprocal both sides.
 
KevinPaul06 said:
Okay thanks I think I get it.

T= 2π√m/k

(T/2π)2 = √m/k
Probably a typo- you mean [itex](T/2\pi)^2= \left(\sqrt{m/k}\right)^2[/itex]

T2/4π2 = m/k

T2/4π2m = 1/k , then reciprocal both sides.
 

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