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I am double integrating my acceleration to obtain the displacement. However, the displacement looks so strange.

Basically this is the measured acceleration of a system under a impulse movement. and I am trying to obtain it's damping and stiffness properties from this experiment, and that why I would like to have the displacement dataenter image description here

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Looks to me like you have a DC offset to the acceleration data. Try subtracting all acceleration by a constant until you get the first part of Velocity and Displacement to be a horizontal line.

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