Problem: Derive the time period of a simple pendulum using dimensional analysis.

T depends on: length L, mass m, acceleration due to gravity g.

Let T = k * $L^a$ * $m^b$ * $g^c$

Dimensions: [T] = [L]^a * [M]^b * [$LT^{-2}$]^c

For M: 0 = b => b = 0 (T is independent of mass!) For L: 0 = a + c For T: 1 = -2c => c = -1/2 => a = 1/2

Therefore: T = k * sqrt$\frac{L}{g}$

The constant k = 2pi (cannot be found by dimensional analysis). Final: T = 2pi*sqrt$\frac{L}{g}$