The figure shows a pendulum with length L that makes a maximum angle θ 0 with the vertical. Using Newton’s Second Law, it can be shown that the period T (the time for one complete swing) is given by T = 4 L g ∫ 0 π / 2 d x 1 − k 2 sin 2 x where k = sin ( 1 2 θ 0 ) and g is the acceleration due to gravity. If L = 1 m and θ 0 = 42°, use Simpson’s Rule with n = 10 to find the period.
The figure shows a pendulum with length L that makes a maximum angle θ 0 with the vertical. Using Newton’s Second Law, it can be shown that the period T (the time for one complete swing) is given by T = 4 L g ∫ 0 π / 2 d x 1 − k 2 sin 2 x where k = sin ( 1 2 θ 0 ) and g is the acceleration due to gravity. If L = 1 m and θ 0 = 42°, use Simpson’s Rule with n = 10 to find the period.
Solution Summary: The author explains how to calculate the period of the pendulum by using Simpson's rule.
The figure shows a pendulum with length L that makes a maximum angle θ0 with the vertical. Using Newton’s Second Law, it can be shown that the period T (the time for one complete swing) is given by
T
=
4
L
g
∫
0
π
/
2
d
x
1
−
k
2
sin
2
x
where
k
=
sin
(
1
2
θ
0
)
and g is the acceleration due to gravity. If L = 1 m and θ0 = 42°, use Simpson’s Rule with n = 10 to find the period.
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