A computer to be used in a satellite

Question

A computer to be used in a satellite must be able to withstand accelerations of up to 25 times the acceleration due to gravity. In a test to see whether it meets this specification, the computer is bolted to a frame that is vibrated back and forth in simple harmonic motion at a frequency of 7.75 Hz. What is the minimum amplitude of vibration that must be used in this test?

Answer 1

Let

g = 9.81 m/s² be gravitational acceleration,

G = 25g be the target acceleration,

f = 7.75 Hz be the frequency of oscillation,

ω = 2πf be the "angular velocity",

A (to be calculated) be the amplitude.

The position of the oscillating computer as a function of time can be written as

x(t) = Asin(ωt)

If you had calculus then you can calculate the acceleration

a(t) = d²x/dt² = -Aω²sin(ωt)

If you did not have calculus, then I hope you were taught this relation.

So the maximum acceleration is whenever sin(ωt) = ±1.

Equating it to the target acceleration

G = Aω²

A = G/ω² = 25×9.81/(2×π×7.75)² = 0.1 m