A wrecking ball attached to a crane may be thought of as a pendulum. The period of such a pendulum is given (in seconds) by: It 1 P = 4k VI-a²sin²x dx where: a=sin (0/2) e is the angle of the swing (measured in radians from the rest position). k = -√√. ,r is the length of the cable holding the ball, and g is the acceleration due to gravity. Find the period when the following values for 0 = 45°, r = 15 meters, and g= 9.81 m/s². Use Simpson's Rule with 13 panels. Take e = 0.0001. Express the answer with four decimal places.
A wrecking ball attached to a crane may be thought of as a pendulum. The period of such a pendulum is given (in seconds) by: It 1 P = 4k VI-a²sin²x dx where: a=sin (0/2) e is the angle of the swing (measured in radians from the rest position). k = -√√. ,r is the length of the cable holding the ball, and g is the acceleration due to gravity. Find the period when the following values for 0 = 45°, r = 15 meters, and g= 9.81 m/s². Use Simpson's Rule with 13 panels. Take e = 0.0001. Express the answer with four decimal places.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A wrecking ball attached to a crane may be thought
of as a pendulum. The period of such a pendulum is
given (in seconds) by:
11
1
P = 4k √ √1-a²sin²x
dx where: a-sin (8/2)
e is the angle of the swing (measured in radians from
the rest position).
k =
,r is the length of the cable holding the ball,
and g is the acceleration due to gravity. Find the
period when the following values for 0 = 45°, r = 15
meters, and g= 9.81 m/s². Use Simpson's Rule with 13
panels.
Take e = 0.0001. Express the answer with four decimal places.
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