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!

gb7nash
Homework Helper
So you're starting from:

$$T = 2n \sqrt{\frac{m}{k}}$$

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.

HallsofIvy
Homework Helper
If you have c= ab and want to "isolate" b, divide both sides by a: b= c/a.

If have a square root, $y= \sqrt{x}$, square both sides: $x= y^2$

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.

HallsofIvy
Homework Helper
Okay thanks I think I get it.

T= 2π√m/k

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

T2/4π2 = m/k

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