Challenge

Week 3 - Solving second order ODEs

SSatyabrata Rana30 Dec 2022

AIM -

Aim of this Challange is to animate the movement of pendulam by solving the equation of motion of a simple pendulum with damping by using PYTHON.

OBJECTIVE -

The way the pendulum moves depends on the Newtons second law. When this law is written down, we get a second order Ordinary Differential Equation that describes the position of the "ball" w.r.t time.

Objective is to write a program that solves the following ODE. This ODE represents the equation of motion of a simple pendulum with damping

Write a program in PYTHON that will simulate the pendulum motion, then use the information to animate the motion of the pendulum.

THEORY -

Simple Pendulum -

A simple pendulum device is represented as the point mass attached to a light inextensible string and suspended from a fixed support. A simple pendulum shows periodic motion, and it occurs in the vertical plane and is mainly driven by the gravitational force.

It is interesting to note that the time period of the real simple pendulum remains constant even if the amplitude is changed but if the acceleration due to gravity changes the time period of the simple pendulum also changes. This property is also used to determine or verify acceleration due to gravity. The time period also depends on the length of the string to which the Bob of the simple pendulum is attached.

Python Code -