Question

A "shaker table" is a device on which you very securely mount an object and shake it to see if it comes apart under the acceleration due to the shaking. It is widely used to test electronic components to be launched into space to see if they can withstand the acceleration forces that are involved in the launch. The shaking is usually simple harmonic. In operation, such a shaker is started at zero frequency and, while the amplitude is fixed, the frequency is increased. If the amplitude of the shaker is set to 1.80 cm, at what oscillation frequency is the maximum acceleration of the object under test equal to 10.40 g's? (One g is 9.8 m/s²). Give your answer in Hz.

Answer 1

As mentioned in the problem -

Amplitude of the shaker, A = 1.80 cm = 0.018 m

Maximum acceleration of the object under test -

a = 10.40g = 10.40 * 9.8 = 101.92 m/s^2

Suppose, angular velocity of the object = w

So, in the case of simple harmonic motion -

Maximum acceleration is given as,

a = A*w^2

=> 101.92 m/s^2 = 0.018 m * w^2

=> w^2 = 101.92 / 0.018

=> w = 75.25 rad/s

So, the oscillation frequency (f) = w / (2*pi) = 75.25 / (2*3.141) = 12.0 Hz (Answer)