Pendulum - Python Eulers method
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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Question
Pendulum - Python
Eulers method

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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