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I am trying to simulate the following block diagram in Matlab Simulink

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which simulates the equation: $\ddot{y}(t) = - \omega_0^2\ y(t)$ with the second integrator having the initial condition of 1. where this equation can have the solution : $y(t) = cos(\omega_0 t)$

but upon simulation, I got the following result:

enter image description here

I can notice the mathematical solution doesn't follow the actual simulation where the simulation will always produce a sinusoidal trying to reach a stability state which is the oscillation between (inital_condition / 2) and (-inital_condition / 2). So why doesn't the mathematical solution match the simulation

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the problem was with Simulink itself. I had to make the step size constant and very small in the model parameters to catch the whole signal.

enter image description here

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