Week 4.1 - Solving second order ODEs
Report on Solving second order ODEs
Aim:
- To write a program that solves the following ODE. This ODE represents the equation of motion of a simple pendulum with damping
- To animate the motion of the pendulum, as shown in the below figure.
Software used: MATLAB
Code:
ODE Function code:
Explanation:
- b introduces damping, causing the pendulum to slow down over time.
- The pendulum starts from the vertical position (0 radians) with an initial angular velocity of 3 rad/s.
- Creates 500 time points from t=0 to t=10.
- Calls ode45 to solve the pendulum equations.
- Uses the anonymous function @(t,theta) ode_func(...) to pass parameters.
- Plot the graph between Angular displacement vs. time and Angular velocity vs. time.
- For loop is used to animate the pendulum each time.
- (x0, y0) is the fixed pivot point and (x1, y1) is the pendulum bob position.
- line 34 plots the pendulum bob as a red circle.
- line 37 draws the pendulum rod.
- line 38 adds a pivot bar for reference.
Result:
Conclusion:
- The ODE is solved.
- You tube link for an animation - https://youtu.be/otK2GUVfO1M .