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Using Newton's law, we find
m
d2α/dt2 = ma
= Wm
= - mg sin(α)
The minus sign comes because the
restoring force
Wm
is in the direction which is opposite to the displacement.
It follows a second order differential equation in
α
which is given by
d2α/dt2
= - (g/) sin(α)
Unfortunately, this second order differential equation
is way to difficult for us to solve it.
In the following we study an approximation for small angles.
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