Simple Harmonic Motion Problems

[03MGCobra]

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]

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?

 

[03MGCobra]

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]

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.

 

[03MGCobra]

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

 

[gneill]

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.

 

[03MGCobra]

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

 

[gneill]

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

That looks better!

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