A \"shaker table\" is a device on which you very securely mount an object and sh

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 2.40 cm, at what oscillation frequency is the maximum acceleration of the object under test equal to 9.20 g's? (One g is 9.8 m/s2). Give you answer in Hz.

Explanation / Answer

- displacement x= 2.4 sin (omega) t velocity =dx/dt = 2.4 omega cos (omega) t acceleration =dv/dt =- 2.4 (omega)^2 sin(omega)t max value of sin omega t = 1 . replace sin omega t by one in acceleration equation acceleration in g = 2.4 (omega^2)/980 , omega = 2 pi freq 9.2 = 2.4 *(( 2* pi* freq)^2 )/980 freq = sqrt( 9.2* 980 /((2.4*4 * (pi^2))=24.45 Hz

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