Differential Equations for Mechanical Pendulum Oscillations

The main goal of this paper is to analyze the mechanical oscillations of a pendulum using MATLAB software.

There are two main types of mechanical oscillations: frictionless and damped oscillations.

The governing differential equation for frictionless oscillations is:

pendulum oscillation

The governing differential equation for damped oscillations is:

pendulum oscillation assignment

The trapezoidal and Euler methods will be used for the numerical solution by the MATLAB software.

The code is shown below:

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Results:

mechanical oscillations differential equations

damped oscillation equation matlab
As can be seen, the Euler rule provides a more accurate solution than the trapezoidal rule. The damped amplitude of oscillations decreases dramatically, while frictionless oscillations have an infinite time of oscillation and amplitude decrement is absent for them.

The MATLAB software helps thousands of engineers and scientists to deal with their tasks in a comfortable and easy way. It is necessary for technical students to learn more about this software and how to use it for their homework. Here, you can see an example of a differential equation and MATLAB solution for frictionless and damped pendulum oscillations.

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