determine the equation of motion if the spring constant is 4. show what is the maximum amplitude reached by the body in this system. in matlab

The equation of motion for a mass-spring system is given by: m * d^2x/dt^2 + k * x = 0

Where: m is the mass of the body k is the spring constant x is the displacement of the body from its equilibrium position

In this case, the spring constant is 4. Let's assume the mass of the body is 1 kg.

So, the equation of motion becomes: 1 * d^2x/dt^2 + 4 * x = 0

To solve this equation in MATLAB, we can use the ode45 function, which is a numerical solver for ordinary differential equations.

Here is an example MATLAB code to find the equation of motion and determine the maximum amplitude reached by the body in this system:

main.m
% Define the equation of motion as a function handle
equationOfMotion = @(t, y) [y(2); -4*y(1)];

% Set initial conditions: displacement (y1) = 1, velocity (y2) = 0
initialConditions = [1; 0];

% Define the time span for integration
tspan = [0 10];

% Solve the equation of motion using ode45
[t, y] = ode45(equationOfMotion, tspan, initialConditions);

% Retrieve the displacement
x = y(:, 1);

% Find the maximum amplitude
maximumAmplitude = max(abs(x));

% Plot the displacement versus time
plot(t, x);
xlabel('Time');
ylabel('Displacement');
title('Motion of the Mass-Spring System');

% Display the maximum amplitude
disp(['Maximum Amplitude: ', num2str(maximumAmplitude)]);
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When you run this code, it will display a plot showing the displacement of the body as a function of time, and also print the maximum amplitude reached by the body in the command window.

Note that the maximum amplitude depends on the initial conditions and can vary for different scenarios.