Week 3 - Solving second order ODEs

Aim=       Solving second order ODEs

2.  Equation to be used=              

d²θ/dt²+b/m X dθ/dt + g/l X sinθ = 0

where

g = gravity in m/s2,

L = length of the pendulum in m,

m = mass of the ball in kg,

b=damping coefficient.

Values of these parameters is as follow.

L=1 metre,

m=1 kg,

b=0.05.

g=9.81 m/s2.

3. Objective of project=  To execute program for second order of differential equation to represent simple motion of pendulum.

4. Body of contents=

1. First we have to define the initial condition of the pendlum that is its displacement  and velcocity. (angular displacement=0,angular velocity=3 rad/sec )

2. Time range will be 0-20 sec.

3. Ode function has to be created for second order equation mentioned above.

4. Output of function is the integration of time for define function.

5. Plot for same is generated and mentioned in the picture shown below.

Function command for ODE equation-