T= 2pi times the square root of (k/m): need to set K=

[swetpear087]

I need to set to K=

T= 2pi times the square root of (k/m)

 

[soroban]

Re: easy help please

Hello, swetpear087!

\(\displaystyle \text{Solve for }k\!:\;\;T\;= \;2\pi\sqrt{\frac{k}{m}}\)

\(\displaystyle \text{We have: }\;2\pi\sqrt{\frac{k}{m}} \;=\;T\)

\(\displaystyle \text{Divide by }2\pi\!:\quad \sqrt{\frac{k}{m}} \;=\;\frac{T}{2\pi}\)

\(\displaystyle \text{Square both sides: }\;\left(\sqrt{\frac{k}{m}}\right)^2 \;=\;\left(\frac{T}{2\pi}\right)^2 \quad\Rightarrow\quad \frac{k}{m} \;=\;\frac{T^2}{4\pi^2}\)

\(\displaystyle \text{Multiply by }m\!:\quad k \;=\;\frac{mT^2}{4\pi^2}\)