damped oscillation in matlab

To simulate and plot a damped oscillation in MATLAB, you need to solve a second-order homogeneous differential equation of the form:

main.m
y'' + 2*b*y' + w^2*y = 0
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Here, y is the amplitude of the oscillation, b is the damping coefficient, and w is the natural frequency of the oscillation.

You can use the built-in function ode45 to solve the differential equation numerically. Here's an example code that simulates and plots a damped oscillation:

main.m
% parameters
b = 0.1; % damping coefficient
w = 1; % natural frequency

% initial conditions
y0 = 1; % initial amplitude
v0 = 0; % initial velocity

% time span
tspan = [0, 20];

% differential equation
ode = @(t,y) [y(2); -2*b*y(2) - w^2*y(1)];

% solve the differential equation
[T, Y] = ode45(ode, tspan, [y0; v0]);

% plot the solution
plot(T, Y(:,1));
xlabel('Time');
ylabel('Amplitude');
title('Damped Oscillation');
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In this code, we define the parameters b and w, as well as the initial conditions y0 and v0. We also define the time span tspan.

Next, we define the differential equation using an anonymous function ode, which takes a time t and a state vector y as inputs, and returns the derivative of the state vector at that time.

We then use the ode45 function to solve the differential equation numerically. This function returns two arrays T and Y, which contain the time and state vector values at each time step.

Finally, we plot the amplitude of the oscillation over time using the plot function.

This should give you a basic idea of how to simulate and plot a damped oscillation in MATLAB.