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Pendulum - Python  Eulers method

Pendulum - Python  Eulers method

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Pendulum - Python 

Eulers method 

Pendulum - Python The motion of a single, undamped (i.e. no friction) pendulum may be described through the ordinary differential equations are: +9/lsin(0) -0, where 8 is the angle between the pendulum and vertical, g is the strength of gravity and I is the length of the pendulum. d²0 dt² MREMA ng cub Force diagram for pendulumn ® Undamped pendula are somewhat unnatural since, given a small push, they continue to swing forever! We rewrite as first order system: 80 Ot dv Ət -g/l sin(8). Through the question we will fix g = 1 = 1 . (We pretend we are living in a world without units!). Q) Implement the system of ordinary equations using Euler's method subject to the initial conditions 0 = 0 and v=vat t = 0. and implement the system of ordinary equations using Euler's method subject to the initial conditions dt = 6/200,00 = 0, v = 1 until T = 6. Make two plots, one which shows the x-coordinate against the y-coordinate and another that shows time t against 8.
Transcribed Image Text:Pendulum - Python The motion of a single, undamped (i.e. no friction) pendulum may be described through the ordinary differential equations are: +9/lsin(0) -0, where 8 is the angle between the pendulum and vertical, g is the strength of gravity and I is the length of the pendulum. d²0 dt² MREMA ng cub Force diagram for pendulumn ® Undamped pendula are somewhat unnatural since, given a small push, they continue to swing forever! We rewrite as first order system: 80 Ot dv Ət -g/l sin(8). Through the question we will fix g = 1 = 1 . (We pretend we are living in a world without units!). Q) Implement the system of ordinary equations using Euler's method subject to the initial conditions 0 = 0 and v=vat t = 0. and implement the system of ordinary equations using Euler's method subject to the initial conditions dt = 6/200,00 = 0, v = 1 until T = 6. Make two plots, one which shows the x-coordinate against the y-coordinate and another that shows time t against 8.
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