the maximum platform displacement x can be computed by equating the change in the weights gravitational potential energy (h + x)∙w with the potential energy stored in the springs in matlab

To compute the maximum platform displacement x, we can use the principle of conservation of energy. We equate the change in gravitational potential energy of the weight (h + x)∙w with the potential energy stored in the springs. We can express this mathematically as:

main.m
0.5 * k * x^2 = (h + x) * w * g
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Here, k is the spring constant, x is the displacement of the platform, h is the initial height of the weight above the platform, w is the weight of the object, and g is the acceleration due to gravity.

We can solve for x using numerical methods in MATLAB. One way to do this is to define a function for the left-hand side of the equation and use a numerical solver to find the root of the function. Here's an example code:

main.m
% Define parameters
k = 100;    % spring constant (N/m)
h = 0.5;    % initial height of weight (m)
w = 10;     % weight of object (N)
g = 9.81;   % acceleration due to gravity (m/s^2)

% Define function to solve
f = @(x) 0.5*k*x.^2 - (h+x).*w*g;

% Use fzero to find root of function
x = fzero(f, 0);

% Display result
fprintf('Maximum platform displacement = %0.2f m\n', x);
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This code defines the parameters and the function f that we want to solve. It then uses the fzero function to find the root of f starting from an initial guess of 0. Finally, it displays the maximum platform displacement.