# What's the meaning of 'Total acceleration effective'?

I'm reading a document describing the procedure to do a random vibration test. In it, a PSD (Power Density Curve) curve is defined, and there's a note at the bottom of the curve:

Total acceleration effective: 50 to 500 Hz = 2.0G


What does it mean? Thanks.

For a discrete system with $$N$$ degrees of freedom, the displacement can be expressed as $$\mathbf{u}(t) = \sum_{i=1}^N \boldsymbol{\Phi}_i \Gamma_i s_i(\omega_i, t)$$ where $$\boldsymbol{\Phi}_i$$ is the mode shape, $$\Gamma_i$$ is the participation factor, and $$s_i$$ is a function of the modal frequency, $$\omega_i$$.
The second derivative of the displacement, $$\ddot{\mathbf{u}}$$ (with respect to time, $$t$$) gives the total acceleration. Some corrections are needed when all the $$N$$ modes are not known.
To get the g value, the acceleration ($$\ddot{\mathbf{u}}$$) is divided by the acceleration due to gravity.