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The trajectory of the mass is along the circle
with radius
which is the length of the string.
When the displament angle equals
α,
then its displacement u,
measured along the circle, equals
u = radius × angle (in radians)
= α
When the mass is in movement,
then α
is a function of the time t:
α=α(t).
For the acelleration we obtain thus
a =
d2u/dt2
=
d2α/dt2
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