Simple Harmonic Motion Problems

AI Thread Summary
The discussion focuses on solving for the spring constant k in the equation T = 2π√(m/k). Participants clarify that squaring both sides of the equation requires squaring all components, including 2π, leading to T² = 2π²(m/k). The correct rearrangement results in k = (2π)²m/T². The final simplified form presented is k = ((2π)/T)²m, which is deemed clearer. The conversation emphasizes the importance of maintaining balance in algebraic equations during manipulation.
03MGCobra
Messages
4
Reaction score
0
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.
 
Physics news on Phys.org
03MGCobra said:
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?
 
03MGCobra said:
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
 
03MGCobra said:
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
 
03MGCobra said:
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
 
Back
Top