Question

Military specifications often call for electronic devices to be able to withstand accelerations of 10 g. To make sure that their products meet this specification, manufacturers test them using a shaking table that can vibrate a device at various specified frequencies and amplitudes. If a device is given a vibration of amplitude 5.6 cm, what should be its frequency in order to test for compliance with the 10 g military specification? The acceleration of gravity is 9.81 m/s2. Answer in units of Hz.

Answer 1

The restoring force on a SH oscillator is proportional of small displacement mad to its position of rest (mean position), which then oscillates about this position, with angular speed, which relates to the instruments natural frequency (in turn related to its stiffness)

acceleration = - (k / m) x = - (w)^2 x
----------------------------------
w = 2 pi frequency = sqrt(k/m)
x = small amplitude or disp, k = stiffness const and m=mass
-------------------------------
magnitude considered
10 g = w^2 * 0.056
w = sqrt [10*9.81 / 0.056]
f = w/2pi = (1/2pi) sqrt [10*9.81 / 0.056]
f = 6.664 Hz
under given virbration of amplitude, test should comply with f = 6.664 HZ