Question

A computer to be used in a satellite must be able to withstand accelerations of up to 24 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 7.21 Hz. What is the minimum amplitude of vibration that must be used in this test?

Answer 1

Answer:

The required amplitud is 0.11cm

Explanation:

To solve this problem it is necessary to apply the concepts related to simple harmonic motion, where displacement is given by

$x = A cos(2\pi ft)$

Where,

A = Amplitude

f = Frequency

t = time

If we derivate the expression we can obtain the Acceleration, there

$\frac{d^2x}{dt} = -(2\pi f)^2 x$

$a = -(2\pi f)^2 x$

x would be A for the minimum amplite of vibration, then

$a = -(2\pi f)^2 A,$

$A = \frac{-(2\pi f)^2}{a}$

Replacing with out values,

$A = \frac{-24*9.8}{(2\pi*7.21)^2}$

$A = -0.1146cm$

Therefore the required amplitud is 0.1146cm