# The time period of a pendulum is `T = 2*pi*sqrt(L/9.8)` . Write in function notation. What is the range and domain. For what value of L is T = 10 s.

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justaguide | Certified Educator

The time period of a pendulum with length L is given by `T(L) = 2*pi*sqrt(L/9.8)`

The length of a pendulum cannot be negative, and neither can the time period. The domain of the function is `[0, oo}` and the range is also `[0, oo}` .

If T = 10, the corresponding value of L is determined by solving:

`10 = 2*pi*sqrt(L/9.8)`

=> `sqrt (L/9.8) = 5/pi`

=> `L = (25*9.8)/pi^2`

=> `L ~~ 24.82` m