Why is this answer wrong?

Question

Military specs oftan call for electronic devices to be able to withstand accelerations of 10 g. To make sure that they do, manufacturers test them using a shaking table that can vibrate a device at various specified frequencies & amplitudes. If a device is given a vibration of amplitude 9.7 cm, what should its frequency be in order to test for compliance with the 10 g requirement (ans in Hz)?

d = v*t + 0.5*a*t^2 = 9.7sin(x*t)
take the derivative
v + a*t = 9.7x*cos(x*t)
take the derivative
a = 9.7*x^2*-sin(x*t)

so:
10g = 9.7*x^2
x^2 = 10*9.8/9.7
x = 10.1

2pi = 10.1*T
T = 0.62 sec

freq = 1/T
freq = 1/0.62
freq = 1.61 Hz

Answer 1

Since it is the case of simple harmonic motion, the equations of motion will not hold good here.
The maximum acceleration in this case is given by
a = r ω^2 ; r = amplitude(0.097m) ,
ω = angular frequency , a = 10 g
=> a = 4π r f^2 ; f = frequency
=> f = sqr root ( 10 g / 4πr)
use this formula. use only S.I. units and you will definitely get the answer

Answer 2

I think you are mixing units.
9.7 cm/sec vs. 9.8 meters/sec.
Change centimeters into meters, and I'll bet it will be OK.