1. The problem statement, all variables and given/known data 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? 2. Relevant equations T= 2∏√(l/g) also l is original length and l+3 is the new length 3. 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.