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## 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.