Scaling factor of a simple pendulum between length and time period.

[mrcotton]

Homework Statement

The time period of a simple pendulum is doubled when the length of the pendulum is increased by 3.0m. What is the original length of the pendulum?

Homework Equations

T= 2∏√(l/g)
also l is original length and l+3 is the new length

The Attempt at a Solution

So
2T=2(2∏√(l/g)
2T=2∏√(4l/g)
The new length is 4 times the original length and it also has to be the original length plus 3m.
∴ 4l=l+3
so l=1m

I am happy with the mathematical steps, and it gives me the correct answer.
It is the reason why I can do this I could do with some guidance on.
Is it because when I double T the only thing that could change is the length?
Therefore I can put the multiplying factor of 2 inside the sqrt as 4×l.

 

[tiny-tim]

hi mrcotton!

It is the reason why I can do this I could do with some guidance on.
Is it because when I double T the only thing that could change is the length?
Therefore I can put the multiplying factor of 2 inside the sqrt as 4×l.

yes, that's exactly right …

T = 2π√(l/g) means that T is proportional to √l, so twice T means 4 times l (if everything else is the same)

(and your proof is completely correct)

 

[rude man]

What you did is fine. But you were lucky to have been able to sneak the "2" inside the square root sign so easily to make 4.

I would have said

T = 2π√(l/g)
2T = 2π√[(l+3)/g]
so 2 = √[(l+3)/l]
& solve for l.

 

[tiny-tim]

isn't that the same?

 

[mrcotton]

Thanks ever so much for the help with getting my old grey matter working.
So in general I can solve it like this.

Did the sqrt of 4 only work for those values.
I tried doing the calculation both ways for a pendulum that's time period has tripled when the original length is extended by 6m and got the same results.

 

[rude man]

Yeah, maybe I was a bit severe here ... did you try for new l = 1.73l? This is a very trivial point, should probably not even have raised it.

 

[mrcotton]

Hi Rude man, please I like the trivial points. Its the pedantic points in physics that make it interesting to me. Each physics question seems to open up more questions.

 

[rude man]

Hi Rude man, please I like the trivial points. Its the pedantic points in physics that make it interesting to me. Each physics question seems to open up more questions.

OK I got plenty of those ...