The equation for the time period of a pendulum is given by
We need to evaluate the percentage error in the measurement of the time period
First, let's consider
These are two values being divided, so their percentage errors should be added together:
Then, let's consider
This expression can be rewritten as
When raising values to a power, we multiply the percentage error by that power:
Now, let's consider
When a value is multiplied by a constant, we multiply the absolute uncertainty by the constant as well.
However, when dealing with percentage errors, we leave it as it is.
So we do not need to multiply the percentage error by the constant.
Therefore, the percentage error in the measurement of the time period of the pendulum is