The pivot point of a simple pendulum of mass
m
and length
l
moves in the
y
-directions according to
y=f(t)
as shown in the figure. Using D'Alembert's principle and the Lagrangian dynamics show that the motion of the pendulum is same as that of a simple pendulum in a gravitational field
g+(d^(2)f)/(dt^(2))
, where,
g
is the acceleration due to gravity.

Question

The pivot point of a simple pendulum of mass

m

and length

l

moves in the

y

-directions according to

y=f(t)

as shown in the figure. Using D'Alembert's principle and the Lagrangian dynamics show that the motion of the pendulum is same as that of a simple pendulum in a gravitational field

g+(d^(2)f)/(dt^(2))

, where,

g

is the acceleration due to gravity.

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