The period P of a pendulum depend on its length, mass as well as the acceleration due to gravity. Use dimensional analysis to show that equation for P has the form

=√

where is a dimensionless costant.

Period P has units of seconds (s).

Length has units of meters (m).

Mass has units of kilograms (kg).

Acceleration has units of meters per second squared (m/s²).

Dimensional analysis:

s = √ (m / (m/s²))

Therefore:

P = k √ (L/g)

where k is a dimensionless constant.