The velocity equation is determined by taking the time derivative
of the displacement equation,
dy/dt = -20 ωn sinωnt
Likewise, the acceleration equation is found taking the second time derivative of the displacement,
d2y/dt2 = -20 ωn2 cosωnt
Therefore, the maximum acceleration is directly related to the square of the natural frequency, or
This can be converted to g forces by dividing by the acceleration of gravity,
gmax = 20/32.2 ωn2 = 0.621ωn2 g's
The motion of the platform and its acceleration are plotted at the left for the two spring constants of 5,000 and 10,000 lb/ft.
The 10,000 lb/ft case is unacceptable since the acceleration exceeds the safety limit of 4 g's.