Quations (3.4) and (3.5) are equivalent expressions for Lagrange's equations.
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The period of a pendulum is given by
where L is the pendulum length and g is the gravitational acceleration.
We can write down the ratio between the period of the pendulum on the Moon and on Earth by using this formula, and we find:
where the labels m and e refer to "Moon" and "Earth".
Since the gravitational acceleration on Earth is
while on the Moon is 
, the ratio between the period on the Moon and on Earth is
where L is the pendulum length and g is the gravitational acceleration.
We can write down the ratio between the period of the pendulum on the Moon and on Earth by using this formula, and we find:
where the labels m and e refer to "Moon" and "Earth".
Since the gravitational acceleration on Earth is