# Simple Harmonic Motion Problems

I am having a hard time solving for k in the equation
T =
2 x pi sq. rt. (m/k)

I know this is simple algebra but its keeping me from solving this.

gneill
Mentor
I am having a hard time solving for k in the equation
T =
2 x pi sq. rt. (m/k)

I know this is simple algebra but its keeping me from solving this.

What happens if you square both sides of the equation?

the sq rt goes away on the side with 2 x pi (m/k) and then T^2. so T^2 = 2pi x (m/k) now can be simplified into k = (2pi x m) / T^2?

gneill
Mentor
the sq rt goes away on the side with 2 x pi (m/k) and then T^2. so T^2 = 2pi x (m/k) now can be simplified into k = (2pi x m) / T^2?

No, you can't just square part of a side. The $2 \pi$ has to be squared, too.

T^2 = 2pi^2 x (m/k) then k = 2pi ^2 x m/ T^2

gneill
Mentor
T^2 = 2pi^2 x (m/k) then k = 2pi ^2 x m/ T^2

What about the 2? You must do the same operation to all parts of a given side if the equation is to remain balanced.

k =((2pi)^2 x m)/T^2

gneill
Mentor
k =((2pi)^2 x m)/T^2

That looks better!

If you want to clean it up a bit, you could make it:
$$k = \left( \frac{2 \pi}{T} \right)^2 m$$