# Differentials find maximum percentage error

1. Nov 23, 2009

### naspek

1. The problem statement, all variables and given/known data
The period T of a simple pendulum with small oscillations is calculated from the
formula T = 2pie (L / g)^1/2 . Suppose that measurements of L and g have errors of at
most 0.5% and 0.1% respectively. Use differentials to approximate the maximum
percentage error in the calculated value of T.

3. The attempt at a solution
dT = (dT/dL)dL + (dT/dg)dg
= 2pie (1/2g(L/g)^1/2) dL + 2pie (1/2g(L/g^2)^1/2) dg
i dont know how am i going to proceed..

2. Nov 23, 2009

### Staff: Mentor

You're not using the chain rule correctly. Also, the name of the Greek letter is pi, not pie.
dT/dt = d/dt(2 pi sqrt(L/g)) = 2 pi d/dt( L^(1/2)/g^(1/2))
Now use the quotient rule to complete the differentiation on the right. After you get that, you can multiply both sides of your equation by dt to get an equation that involves dT, dL, and dg.

3. Nov 23, 2009

### naspek

ok.. got it already.. maximum percentage is 1.2% ^_^