How Many Pendulum Periods Minimize Time Uncertainty in Gravity Calculations?

[nubey1]

Homework Statement

The length of a string attached to a pendulum is measured with a precision of (+or-)0.2. The time of the oscillation is measured to a precision of (+or-)0.1. How many periods must you measure so that the contribution of the uncertainty in time is smaller than the uncertainty in length, when calculating g?

Homework Equations

T=2pi(l/g)^(1/2)

The Attempt at a Solution

g=((2pi)^2(l+delta:l))/(T+delta:T)^2
I don't know where to go from here.
Delta l and T are the error in those measurements.

 

[dark adonis]

Homework Statement

The length of a string attached to a pendulum is measured with a precision of (+or-)0.2. The time of the oscillation is measured to a precision of (+or-)0.1. How many periods must you measure so that the contribution of the uncertainty in time is smaller than the uncertainty in length, when calculating g?

Homework Equations

T=2pi(l/g)^(1/2)

The Attempt at a Solution

g=((2pi)^2(l+delta:l))/(T+delta:T)^2
I don't know where to go from here.
Delta l and T are the error in those measurements.

The next thing to do is assume that the error is really small relative to the actual value.
$$\delta l << l$$ and $$\delta T << T$$. I think you might have an error in your equation for g:
$$g +\delta g= (2 \pi)^2 \frac{l+\delta l }{(T+\delta T)^2}$$ where $$\delta g$$ is the error in g.
If you are familiar with calculus then this comes out to:
$$\delta g = |\frac{\partial g}{\partial l}| \delta l + |\frac{\partial g}{\partial T}| \delta T$$
If you don't have the luxury of calculus we might need to know what relations for uncertainty you are given to clue you in