- #1
StevenJacobs990
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The equation for large-angle pendulum can be infinitely long. What is the pattern with the latter numbers in "..."?
In summary, the conversation discusses the equation for large-angle pendulum and the lack of pattern in the numbers that come after 11/3072 (theta)^4. The attachment provided by one person is not readable, and another person shares a graphic they made. The conversation also mentions equation 3 and the possibility of it being a Taylor expansion. The conversation ends with one person sharing a pendulum calculator they created and inviting others to try it out.
- #2
sophiecentaur
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Sorry, your attachment won't open for me.
- #3
sophiecentaur
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Does this link help?
- #4
StevenJacobs990
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Yeah, but what's the pattern that comes after 11/3072 (theta)^4?sophiecentaur said:
- #5
Vanadium 50
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There is no pattern. That's why you need the elliptic integrals.
- #6
sophiecentaur
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AS I said before, your attachment is not readable.StevenJacobs990 said:
- #7
StevenJacobs990
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This is the attachment
- #8
wolf1728
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Here is a graphic I made.
Look at equation 3.
Look at equation 3.
- #9
wolf1728
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I don't know the equation for generating those numbers in the formula but here is the large amplitude formula carried out to theta 20:
- #10
rumborak
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Honestly, I wouldn't be surprised if this a Taylor expansion of some sort.
- #11
sophiecentaur
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. . . .or something else. There are (my Mathematician friends tell me) many equations that can only be solved using a series - Taylor or not so well known ones.rumborak said:
- #12
wolf1728
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I originally was writing a pendulum calculator and while researching the Internet, I came across this topic. Anyway, I finished the calculator and it is online: http://www.1728.org/pendulum.htm
It can calculate pendulum periods up to theta 14 and uses the arithmetic mean to calculate exact pendulum periods.
Try it out if you like.
It can calculate pendulum periods up to theta 14 and uses the arithmetic mean to calculate exact pendulum periods.
Try it out if you like.
Related to Large Amplitude Pendulum Equation
1. What is the Large Amplitude Pendulum Equation?
The Large Amplitude Pendulum Equation is a mathematical equation that describes the motion of a pendulum when the angle of displacement is large, typically greater than 10 degrees. It takes into account the effects of gravity, the length of the pendulum, and the mass of the object at the end of the pendulum.
2. How is the Large Amplitude Pendulum Equation derived?
The Large Amplitude Pendulum Equation is derived from the simple pendulum equation by considering small angle approximations and using the Taylor series expansion. This allows for a more accurate representation of the pendulum's motion at larger angles of displacement.
3. What are the applications of the Large Amplitude Pendulum Equation?
The Large Amplitude Pendulum Equation has many applications in physics and engineering. It is used to study the behavior of pendulums in various systems, such as clocks, seismometers, and amusement park rides. It is also used in the construction of tall buildings and bridges to ensure their stability against wind and earthquakes.
4. What factors affect the motion described by the Large Amplitude Pendulum Equation?
The motion described by the Large Amplitude Pendulum Equation is affected by several factors, including the length of the pendulum, the mass of the object at the end, the initial angle of displacement, and the acceleration due to gravity. Changes in these factors can alter the period and amplitude of the pendulum's motion.
5. How is the Large Amplitude Pendulum Equation different from the Simple Pendulum Equation?
The Large Amplitude Pendulum Equation differs from the Simple Pendulum Equation in that it takes into account the effects of larger angles of displacement. The Simple Pendulum Equation assumes that the angle of displacement is small, and therefore, it is only accurate for small oscillations. The Large Amplitude Pendulum Equation provides a more accurate representation of the pendulum's motion at larger angles of displacement.
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