# Math Help - Calculus - Error

1. ## Calculus - Error

The time of oscillation, T seconds, of a simple pendulum is very nearly equal to 2/L , where L is the length of the pendulum in metres. A pendulum is made to have a time of oscillation of 1 second. Find the effect on the time, if there is an error of 2mm in the length.

2. This is my solution, somehow answer is different when I calculate without using calculus.

${\delta L} = 2mm = 0.002m$

$\dfrac{dT}{dL}\approx\dfrac{\delta T}{\delta L}$

${\delta T} = \dfrac{\delta T}{\delta L} * {\delta L}$

${\delta T} = \dfrac{-2}{L^2} * 0.002$

${\delta T} = \dfrac{-0.004}{L^2}$

Given that oscillation time, T = 1 second, so L = 2m

${\delta T} = \dfrac{-0.004}{2^2}$

${\delta T} = -0.001s$

But, the answer given is 0.004s longer.

Can someone check if my working is right?