I'm completly stumped by this one. Any help would be deeply apreciated.
T=2*pi*the square root of m/g
the problem asks you to solve for g.
Thanks in advance.
do you mean $\displaystyle T = 2 \pi \sqrt {\frac mg}$ ?
if so, $\displaystyle T = 2 \pi \sqrt {\frac mg}$ ..........divide both sides by $\displaystyle 2 \pi$
$\displaystyle \Rightarrow \frac T{2 \pi} = \sqrt {\frac mg}$ ............square both sides
$\displaystyle \Rightarrow \left( \frac T{2 \pi} \right)^2 = \frac mg$ ..........flip both sides and multiply by m
$\displaystyle \Rightarrow g = \frac {m}{\left( \frac T{2 \pi} \right)^2} = \frac {4 m \pi^2}{T^2}$
$\displaystyle t=2\pi\sqrt{\frac{m}{g}}$
Dividing both sides by $\displaystyle 2\pi$:
$\displaystyle \frac{t}{2\pi}=\sqrt{\frac{m}{g}}$
Squaring both sides:
$\displaystyle \frac{t^2}{4\pi^2}=\frac{m}{g}$
Reciprocating both sides:
$\displaystyle \frac{4\pi^2}{t^2}=\frac{g}{m}$
Multiplying both sides by m:
$\displaystyle \frac{4\pi^2m}{t^2}=g$
$\displaystyle g=\frac{4\pi^2m}{t^2}$
We can make this more specific by recognising in the original equation that t cannot be $\displaystyle < 0$, since $\displaystyle 2\pi\sqrt{\frac{m}{g}}$ cannot be negative. So we have:
$\displaystyle g=\frac{4\pi^2m}{t^2} \ \text{ and } \ t\geq 0$