- #1
Dustinsfl
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Homework Statement
An electromagnetic fatigue-testing machine has an alternating force is applied to the specimen by passing an alternating current of frequency ##f## through the armature. If the weight of the armature is ##40## lb, the stiffness of the spring ##k_1## is ##10217.0296## lb/in, and the stiffness of the steel specimen is ##75\times 10^4## lb/in, determine the frequency of the alternating current that induces stress in the specimen that is twice the amount generated by the magnets.
Homework Equations
##m\ddot{x} + (k_1 + k_2)x = F_0\sin(\omega t)##
The Attempt at a Solution
I have found the equation of motion:
$$
x(t) = A\cos(431.571t) + B\sin(431.571t) + \frac{F_0/m}{431.571^2 - \omega^2}\sin(\omega t)
$$
where ##m = W/g = 4.08163## and ##\omega_n = \sqrt{\frac{k_1 + k_2}{m}} = 431.571##.
The answer is ##f = 743.7442## Hz. I have no idea how I am supposed to obtain this answer. I know if I can find ##\omega##, then ##f = \frac{\omega}{2\pi}##, but I don't know how can I can go about finding ##\omega##.