the time period T for a simple pendulum of length l is given by T=2π⋅√(l/g) where g is a constant.

Question

find the percentage change in T when l changes by 6%

Answer 1

taking derivatives, you have

dT = π/√(gL) dL

Now, to find the % change of T, you take

dT/T

You would expect it to be about 1/2 the change in L, since you have roughly

T^2 = kL
2T dT = k dL