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![Getting Outputs
Use the following command in the Command Window
to get the outputs.
First code calls func1 and gives the outputs value
matrix [t, x].
Under the ode45() code, [0 10] gives time of run i.e. 0
to 10 seconds and [7 4.3] gives initial conditions of
𝑥1 (0) = 7 and 𝑥1(0) = 4.3.
Subplot() command is used to create multiple plots in
the same figure.
Third code gives the graph for time vs displacement of
the bob.
Hold on code is used to plot two
plots in one graph.
xlabel and ylabel codes are use to
label the axes in the graph.
Second last code gives the phase
trajectory for the pendulum.](https://image.slidesharecdn.com/analysingsimplependulumusingmatlab-170407193245/85/Analysing-simple-pendulum-using-matlab-5-320.jpg)
Uploaded byAkshay Mistri
Analysing simple pendulum using matlab
This document describes how to analyze a simple pendulum using MATLAB. It contains the equation of motion for a simple pendulum, notes on defining the equation in MATLAB, instructions for defining the two equations in a script file in MATLAB, and commands for running the code to output graphs of displacement over time and a phase trajectory plot.
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Analysing simple pendulum using matlab
- 1. Analysing Simple Pendulum usingMATLAB CREATED BY: AKSHAY MISTRI
- 2. Equation of Motionfor Simple Pendulum 𝐷2 𝑥 𝐷𝑡2 + 𝑔 𝑙 *sin(𝑥) = 0 D in the equation represents differentiator function. There is no friction/energy loss. (Infinite oscillations) Rod always remains taut. 𝑥 : angular displacement of the bob. 𝑙 : length of the rod. 𝑔: acceleration due to gravity. (𝑚/𝑠𝑒𝑐2)
- 3. Things to Note Matlab can solve linear differential equations much easily. Hence, we will convert the pendulum equation to linear form and then define it in matlab code. When we convert the pendulum’s second order differential equation to linear form, we get two equations in 𝑥1 and 𝑥2 which are actually displacement 𝑥 and velocity of the bob. So, we write 𝑥1 = 𝑥2 (Equation No.1). Therefore, 𝑥1 = 𝑥2 = - 𝑔 𝑙 *sin(𝑥), using pendulum’s equation of motion (Equation No.2).
- 4. Defining the twoequations in MATLAB We define the equations in a script file, which can be called when running the code. To make a script file, first create a folder in matlab using >>mkdir pendulum and go into that folder using code >>chdir pendulum. (mkdir: make Directory; chdir: change Directory). Now create a script file using command >>edit func1.m , it will give you a message that the file does not exist and do you want to create it? Then click on yes. As the script file opens, type the given command as shown in the picture. Please note, I have taken length of the rod to be 1 metre. Last step in the picture returns the value of xdot as a column vector. It is very important to keep the function name and script file name same.
- 5. Getting Outputs Usethe following command in the Command Window to get the outputs. First code calls func1 and gives the outputs value matrix [t, x]. Under the ode45() code, [0 10] gives time of run i.e. 0 to 10 seconds and [7 4.3] gives initial conditions of 𝑥1 (0) = 7 and 𝑥1(0) = 4.3. Subplot() command is used to create multiple plots in the same figure. Third code gives the graph for time vs displacement of the bob. Hold on code is used to plot two plots in one graph. xlabel and ylabel codes are use to label the axes in the graph. Second last code gives the phase trajectory for the pendulum.
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